What is a better approach to learning Greek...?
Would it be better for me to go through the tree at a relatively quick pace and then get most of my learning from consistently reviewing it, or would it be better for me to take the tree extremely slowly and make sure that I understand absolutely everything before moving on?
I'd say the first option is better. Taking the tree extremely slowly has a disadvantage of it being extremely boring. Also due to the fact that you don't know much grammar in the first few chapters, some of the stuff at the beginning of most language trees is full of things that you will probably never even NEED to say, things like "The elephant is pink." - I don't even remember the last time I uttered the word "elephant" in my native language, let alone in my target language. So, it's good to skim through the skills like animals or colours, but time would be better spent on some of the more important stuff that you'll only find further down in the tree; perhaps a useful expression, or a verb that's going to come in handy in countless situations, and so on. I'd say: go through the tree at a quick pace, and then rework on the skills that you feel like you need a practice in.
You can finish the Greek tree even with just a few thousand xp and in level 10. But it does not mean you know the language. Strengthening a tree is the most important. Learning a language with DL is a long-term process, as in every language. Level 25 can be reached after a long try, when xp's are about 30.000-35.000, that means you have finished 3000-3500 exercises. Is it boring? Yes, in a way. But you can change languages with DL and this makes it fascinating.