If you live in the US the RX 460 is a really nice card for the money. I think your system is fine for esport games since you will most likely have certain things turned down or off anyways to reduce input delay anyways. I think if you try to play games mores intensive you might run into some problems. Like my my old htpc had a 3870k 'The first gen quad core apu' and a 750 ti which got upgraded to the gtx 950, I have that one relocated downstairs now as kind of like a 2nd htpc. But that thing while not being able to max out games and be at a stable 60 fps it still only has a major dip every once in a while down to like 35 with a mix of mid to high settings on some of the newer games. But it stays around 45+ most of the time.
So if it was up to me I would go for the rx 460 or 560, if you have the budget and power supply maybe go for the 470 or 570. You can always just upgrade the cpu/board down the road. But I'm guessing you aren't a max out everything gamer anyways so I'm sure you will be happy with either.