From the pic of your compressor above, I'd say it is adequate to handle a HVLP gun w/ no issues. That's the same size I have been using for many years, and I spray almost every project.
If you haven't done a lot of HVLP spraying in the past, and are just kinda getting your feet wet (no pun intended), I would suggest one of two routes to get started. First, visit another member w/ a set-up and try it out. Take a quart of the type of finish you would like to spray, along w/ a couple of boards, and see how you like it. If you don't want to use someone else's equipment, buy a cheap HVLP gun at Harbor Freight (under $15 w/ a coupon) and try it at home. I wouldn't consider this a long term solution, but it's a good way to test the waters.