Greek
Koine Greek is the language of the New Testament, and if New Testament Greek is all you're planning on working with, your journey won't be terrible. In any language, there's only so much morphology, only so much syntax, though a tremendously more than morphology, but an absolute ocean of words. Words become the endless journey of life. There are only so many words -- it's not like you need to learn the words for carburetor, pizza, and keyboard. The scope is limited. In fact, most Koine Greek studies are on syntax. What's called "first year studies" is morphology, with the rest being all syntax.
When you first learn New Testament Greek, you always always learn the Greek of John's corpus first, that is, you start with "baby Greek". This is how I learned, but I don't find it to be the most optimal. I should have learned something like Attic Greek either along side of Koine or prior to Koine.. This isn't so much because attic or Homeric Greeks are so much more important, but because that's where the good resources are, both in introductory resources, and in deeper studies. More importantly, I think an early focus on Attic would have prepared me better for Luke, Acts, and Hebrews. Up till those, books you've still got the training wheels of prepositions, articles, and shorter statements. When you get to those books, you're swimming in participles. Going from John to Paul isn't that big of a deal, but jumping from there to Luke can be somewhat of a shock.
The goal of studying Greek has changing in the past few years with deeper understanding of linguistics and psychology. How so? Much language study in the past century or so has been based on enlightenment understandings of studying: soul-crushing paradigm memorization. The approach to language is structures like the approach to math: building brick by brick. Now that we have a better understanding of our phonological loop, and now that we've come to see the common sense notion that no toddler is studying grammar, we can stop micromanaging the brain's acquisition of a language.
Furthermore, 20th century Chomskyan Linguistics has helped the secular world finally catch up with the Christian understanding that we're linguistic creatures. Now that Christians are finally starting to stop cosplaying as secularly 19th century state-controlled secularists, we can finally get back to language acquisition by letting the brain do what God created it to do.
In the end, we're meant to interact with languages constantly and let our brain handle figuring it out -- which is how all kids acquire a language, a model we now call comprehensible input. It's also the primary way most people learn English: someone will wake up in India, realize their future is in the English language, then start watching Netflix until they have it. You learn historical facts, you acquire a language. You study history, you practice a language. While you practice both math 
and a language, math must be done systematically, whereas a language has no order. Throw it all at your brain, and let it figure it out.
Why does any of this matter? The soul-crushing paradigm memorization method is painful. You can avoid this pain by simply learning things in context, which is how we're supposed to do anything. The focus on context not only leads to a better understanding of words, it helps us avoid an incredible abundance of flawed exegesis. Read the following from Intermediate Greek Grammar Mathewson and Emig:
The focus is on individual words and grammatical forms, often at the expense of sensitivity to the broader context in which they occur. Such individual elements of NT Greek are thought to be "rich" in meaning. This can be seen, for example, in approaches that read theological significance out of verb tenses. So we are told that the perfect tense (ἐγήγερται) in 1 Cor. 15:4 is theologically significant because it portrays Christ's resurrection as a reality based on a past action that continues into the present. This theological insight may be valid (in fact, we would insist that it is!), but it is not dependent on a single linguistic unit, the perfect tense-form (nor are we convinced that this is a correct understanding of the perfect tense-form itself). Rather, such insight comes from the broader context of Paul's discussion of the resurrection in 1 Cor. 15. Or how often have we heard the aorist tense, or the genitive case, or prepositions "milked" for theological purposes? We think here of the weight that has sometimes been given to the debate between the "objective" and "subjective" genitive in the expression πίστις Ἰησοῦ Χριστοῦ, It is not that it is unimportant whether we think in terms of faith placed in Jesus Christ or of Jesus' own faithfulness; it is just that our decision in many cases is primarily theological rather than grammatical and should not be based solely on isolated elements such as tenses, cases, or prepositions. Once more, our focus should be on the larger context as the bearer of theology. Any major theological points worth affirming and arguing for will certainly not be nuanced in small grammatical subtleties or fine distinctions between case uses. Rather, they will be clear from their entire contexts. At the heart of this is the failure to recognize how language actually works.
Basics of Biblical Greek Grammar ("BBG"), 2nd edition (Bill Mounce)
Most New Testament Greek texts are horrible, but this may be the least horrible. The author's tips are helpful, especially his tips on what NOT to do while doing your initial studies.
His supplemental materials on his website are also good. Each chapter starts with a paragraph from a different scholar who applies what you'll learn in that chapter to a Biblical text. This is amazing -- examples and reading should always precede analysis.
I used to recommend the 2nd edition, because the 3rd was far too large; however, the author's website mentions that the 4th edition fixes the verb problem. It's no secret that the 1st, 2nd, and 3rd editions taught an absolutely incorrect verbal system, but it seems he fixed it in the 4th edition. Nonetheless, the 2nd is fine, and likely cheaper -- you can reorient yourself on verbal aspect with another resource.
Athenaze (Maurice Balme, Gilbert Lawall)
I wanted to list this one first, but your first resource really should be a Biblical Greek text.
As I've mentioned on my Latin resources page, learning by reading is the way to go. For Latin, it's Lingua Latina, for Greek it's Athenaze. Work through it and let the stories grow your Greek. Ultimately, you want to read the text, then think about what you've read.
This is vastly different than the alternative used in most seminaries: analyze the grammar first, then read a token sample. That's backwards. Slowly work through grammar books under the boot of soul-crushing paradigm memorization is not the key to success. Memorization is easier when you have context. Many words have no direct meaning without context. Context is the structure of Biblical understanding, let's make it the structure of language understanding.
Daily Dose of Greek ("DDG")
DDG is for new folk and seasoned. If you're trying to keep up your Greek, this will help you by helping you read. If you're new, same thing. It's all about reading in context. It doesn't matter if you're new or seasoned. Read more. Read endlessly. Read it again. Much, if not most, of the time, your learning won't come from staring at declensions, it will come from seeing words used in context.
Basics of Biblical Greek Grammar, Workbook
The workbook is fantastic. I buy them in bulk when I see them in Mardel clearance. I go through them every few years to keep my skills polished. You can find the answer key online. Workbooks without answer keys are pointless. You should try to get used if its not marked.
Reading Koine Greek: An Introduction and Integrated Workbook (Rod Decker)
I like to work through a different text every few years -- I did this one a few years ago. It got verbal aspect right on the first publication. The "integrated workbook" is quite anemic.
An Introduction to Biblical Greek: Elementary Syntax and Linguistics (Dana Harris)
I just started working through this one, so I can't review yet, but, when the author gets to verbs, verbal aspect comes up right away. This is critical. There's also a workbook. That said, it's a grammatical piecemeal book, which is unhealthy for anything language related. The author's focus is definitely not the text, but the grammar. Not helpful -- if you can get it for $5, great.
A Reader's Greek New Testament
In BBG, the author tries to get your confidence up by telling you that 80% of the NT is just 300 words. In reality, that means you're looking up every 5th word. Not helpful. However, the Reader's Greek New Testament puts a gloss of the Greek words at the bottom of the page. To use this text, you do need to understand the basics of Greek and a solid vocabulary. Those 80% of those words won't be defined on the page -- that's on you.
Greek Grammar Beyond the Basics (Daniel Wallace)
Most people generally consider this book to go with BBG -- though it's not formally related. After the first few chapters, I generally use it as a reference. Daniel Wallace has one of the wildest life stories I've ever read, you can read about him in Lee Strobel's The Case for the Real Jesus. It's wild.
Intermediate Greek Grammar: Syntax for Students of the New Testament
While not formally linked, this book generally follows the Decker text. You really do need multiple intermediate texts to get an idea of the various ways you can think about the nuances.
Basics of Verbal Aspect in Biblical Greek
One of the wild things about Greek to an English speaker is the importance of verbal aspect (the part of the language BBG got wrong for so long). This book is important to help you avoid pitfalls.
Morphology of Biblical Greek
This is an interesting text for hyper-geeks. If you're curious about the relationship between words, or want a better way to remember an odd form, this book is for you.
Notes
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Speaking of soul-crushing, you don't study math, you practice math just as you practice the violin. This one shift in focus removes much pain in gaining better math skills. I wish my teachers would have told me this decades ago, and I wish their teachers told them.
Speaking of soul-crushing, you don't study math, you practice math just as you practice the violin. This one shift in focus removes much pain in gaining better math skills. I wish my teachers would have told me this decades ago, and I wish their teachers told them.
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