CTA copy works best when it doesn't just describe the process or function, but evokes the advantages or eventual result of that process too. If your app is a social platform, 'join' could do that well. If it's about community action, 'Get involved!' might work too. Of course, your CTA copy should still indicate that a sign up form is forthcoming, else you will frustrate your users and lose their trust.
If 'register' and 'sign up' are your only options? I have never performed an A/B test on registration link copy, but I've always been wary of 'sign up' as it's a little too close to 'sign in' for my liking, which I prefer to 'log in' as it's just a little less technical-sounding. That has usually left me with 'register', which I've never seen users have problems with. I don't think the two terms have any different in concept or tone - theoretically, registration evokes a more formal process, but on the internet they're such common terms for simply 'creating an account' that they've lost almost any other meaning.
As for colour, the typical advice is that humans are better at spotting reds, yellows and oranges than other hues. Yellow against black is particularly noticeable (in nature, lots of dangerous things have yellow-black stripes, which is why hornets don't look friendly) - and, as it happens, works quite well with a black and white colour scheme. Try out combinations with an A/B test, but I think yellow buttons on black would be your ideal solution.