Graphics card availability and pricing changes all the time, and it's been a couple years since I've bought one. I'd say do some research on current budget graphics cards (googling "PC Gamer best graphics cards" is a good start), and then pick one or two and compare their specs to a GTX 970 (which is now 2.5 years old, so it's not a high bar). Not that GTX 970 is the absolute minimum -- I don't know the minimum, but it seems like the GTX 970 is more than sufficient. Use it as a rough reference point, not a hard benchmark. For the games you referenced, you really won't need a heavy-duty graphics card.
Actually, even one of AMD's APUs might be a good idea. I used one of them in a (non-MAME) build a few years ago and was quite happy with it. They're a CPU and GPU in one unit, for a pretty great price.
Also, if you're not used to using cutting-edge stuff already, there's probably no point in worrying about FreeSync. I've never used it myself, so I don't know much about it, but I don't see it being worth it for what you're shooting for. Similar to 4K vs 1080p: If you want to spend the money on it, great, but you can probably get 80% of that performance for 25% of the price.