When I first started I got the Red Sea Marine Care test kit that you are talking about. I highly recommend it and comes with everything you need to start off your cycle and first few months.
After a while you will want to add coral. While the Alk test in the marine care kit will do fine while you are relying on water changes to keep your parameters in check eventually you will need to dose, in which case you will also need to check Calcium and Magnesium (sometimes it could be handy to check them as soon as you start with coral anyway). In that case I would recommend also getting the Red Sea Reef Foundation test kit. That comes with Alk, Cal & Mag and is very cost effective for all of them.
You will also need a way to measure phosphate. I use the Red Sea Pro kit but this one isn't as cost effective as the others. I have heard good things about the salifert kit (cheap), but most people seem to use the Hannah low range checker which is expensive to start with but refills aren't too bad.