Salifert for most. Phosphate I use the Hanna ULR Phosphorus. I usually use Hanna for Alk as well, just because it's a bit simpler to do.
API is ok for what it is, but doesn't handle the lower ranges well for nitrate and phosphate. And I find the color shades for some of the others harder to read than other brands. That could be more about my eyes than the tests, but it seems to be a common view.
Red Sea I've only used a few times. I wouldn't hesitate to buy them either. I like salifert a little better most of the time, but I would use either and feel confident that they would get the job done.
If you know some local refers, ask if they will let you run a test. That way you can see for yourself how they work for you. And you have someone that knows what to expect from the test to help make sure you do it right. The best kit is only as good as the user.