FYI, if you're willing to settle for a drachm, rather than the bigger, flashier tetradrachm, Alexander the Great is actually quite affordable.
I can't help it. Slab fever has me in a strangle hold. I just sent NGC another 8 coins this morning for slabbing and certification. Maybe I need Slabber's Anonymous.
I can completely relate. I still work on my US type set, but I only add to it if I can get the coins for less than half of wholesale. I've tried this with non-collectors. I show them a $2 ancient Chinese Wu Zhu, and they are enamored by it and the history is represents. I show them a picture of a $500 1914 D cent (don't have one, and never will), and they don't understand why it is so valuable. That is my guide for collecting coins: big-picture historical interest. If a coin has a beautiful design, I will give it a pass as well.
I got to the ancient coins through my study of ancient history. I first looked for some ancient coins on the internet when reading a book from Warren Treadgold on Byzantine state and society. The author adresses the coinage and its role in the Byzantine economy very thorougly. When I saw some pictures of actual coins I didn't find them aesthetically pleasing so I let it rest for a while. But later I found some references to masterpieces of ancient celators from Greek Sicily so I had a second look if they did any better than the Byzantines. And oh boy they did. I decided to buy myself some nice specimens. I didnt really know where to start before I stumbled upon an article on Harlan Berk's website titled "Your first 25 silver Greek coins". I liked his reasoning so I decided to complete "the set" sometimes in the future. I never actually did because later I branched out into Romans and you really cant buy them all But I became hooked nevertheless.