I would advise doing them together. Decide what, exactly, that you want, and why. Then look up costs. Also, if there's a brick-and-mortar store somewhere within a reasonable distance, that keeps numerous monitors on display, go there and look at them. You won't be able to game on them, but you'll be able to get a feel for how they look, display quality, etc.
I'm not sure you necessarily need to go higher than 1080p.
Dead wrong. 21 inches is, in my opinion, too small in general. I was using a 27-inch 1920x1080, which looked good. My son had a 24-inch 1920x1080 which was smaller, but looked better not because of the higher pixel density, but because the colors and crispness of that monitor were better.
He currently uses a 34-inch 2560x1080, which looks very nice. The naysayers will say the pixels are too big for that resolution, but, while my eyesight isn't what it should be, his eyesight is very sharp, and we both agree that it looks great.
Everyone's eyes will be different in terms of what they like, or don't like. But "21inches 1080p is enough for almost anyone" is way too big of a blanket statement, and not even close to accurate.
At least at 60Hz, it does. My son's got that card/resolution setup, and there are a couple of games that seem to struggle or be unable to hit 60 fps - he is using an i5-6400, though, so that may be the limiting factor. The only one I can remember the name of off the top of my head is 7 Days To Die, but, we observed that lowering the graphics settings doesn't improve the frame rate, which makes me wonder if it's a CPU issue on that particular title. Can't remember the others, maybe Rainbow 6 Siege is the other that can't hit 60 at that resolution (not sure how high he has the settings on that one).
Generally, I'd say for 2560x1080, I'd recommend a step higher - in the RX 590/GTX 1660/GTX 1660Ti area.