I think the first things you should get are things that don't work well if they don't fit, and are therefore not optimal to rent. That includes your exposure protection (if you aren't warm, you aren't having any fun) and your BCD (if the tank isn't stable, you aren't having fun). The next tier is the things that vary a lot or are complex to use, and are therefore much better to own, so you learn how they work. A computer is top on that list.
If you have a local shop where you can rent well-maintained gear, I think a regulator should be way down the list. They are all very similar, and there are no fit issues.
If you have a local shop where you can rent well-maintained gear, I think a regulator should be way down the list. They are all very similar, and there are no fit issues.