Looks like a train pass for a 25 year old is only $150 for 5 travel days, but I hear the trains don't run everywhere, so would it just be cheaper to take the buses everywhere? And what is the best way to get to and from Greece via Istanbul? Bus/train?
I would not buy the railpass. You would need to take a lot of trains during these five days so that the pass would be profitable. Moreover, as the rail network is not very dense, you will need to supplement it by bus journeys anyway. Or you will miss a lot, such as e.g. the Peloponnese.
I suggest that you first make a list of where you want to go, and then check how it can be done. And then buy tickets (train, bus, ferry, ...) on purpose. With 150 USD you can already get far in Greece and see quite a bit.
A more general remark. Rail passes may look interesting at first sight. However, this may not necessarily be true. It is always interesting to compare passes to point-to-point tickets. You can refer to a discussion on this site or to seat61.com.
Even though I am Greek, I haven't lived there for a long time. Last time I traveled to Greece I also went via Istanbul and took an overnight train from there to Sofia and then a plane down to Athens. Before that, I have take trains between Athens and Thessaloniki (the second largest city) and Athens and Patra (another large city). If you are backpacking and want to see the most beautiful parts of Greece (in my opninon Crete and the Islands and the mountains of central Greece and Peloponese) then you are likely to need to take other means of transportation such as ferries, large boats and busses. I really like trains and dislike busses but the few times I have taken an overnighter in Greece and in Turkey the conditions were like getting yourself in a train for the front in WWII (In fact once I was traveling with soldiers as they get free tickets on the overnighter I think). Both in Greece and the one to Sofia from Istanbul were very slow, not very nice and not very comfortable. I know that the day trains are much better and faster than the all night trains, but I haven't used them much (as back when I was travelling around Greece I was going for the cheapest).
Based on those experiences I can recommend you that, depending on your budget and your travel plan, and whether you dislike buses as much as I do, try the following in order of preference: