It all depends on your vet. Heartguard can 'fail' -- my vet likes to test those on HeartGuard. But I use Interceptor (which has a higher rate of success) so he leaves testing up to me. (I usually do because we do pet therapy and it's one more piece of paper in their 'file' I give to facilities).
the point of testing is to make sure there are no adults -- if for some reason HeartGuard fails then the heartworm may become 'resistant' to the ivermectin and you would need to treat and then sue something different for prevention.
I don't do annual shots -- I have titers done instead for parvo and distemper. discuss with your vet -- I've had too many problems with pets who have had vaccinosis and auto-immune type of problems so I don't want to over-vaccinate.
This year Luna came up low on her distemper titer and Kee came up low on her parvo titer (first time since I've had them that they've titered low) so each of them will get that ONE modified live vaccine.
Rabies -- most states require it for license. Check out what your county/state requires (some states do it by state, some by county). The three year shot is FINE. Actually it usually titers high for many many years, but just watch the site and make sure a lump doesn't develop (massage it daily -- usually one won't develop then).
and congrats on being a careful owner!!!