Regeneration is probably one of the most common and really powerful secondaries that go well with Martial Arts or any other primary set for a couple reasons.
Endurance - Martial Arts is very endurance heavy. Regeneration comes with a endurance regenerating power that is even better than the one you can get in Fitness power pool. Put those 2 powers together and you will rarely have downtime due to no endurance. As anyone can tell you, endurance management is one of the huge and constant concerns in this game, with the other sets you have to become a master tactition in regards to managing and using endurance, otherwise you just end up dead, and that's no fun. You still have some end problems in the very begining but far less than with other sets.
Low Levels - IMO Regeneration is very easy to play at lower levels than alot of the other secondary sets. It's pretty easy to slot, even for new people and it has good usefulness that only gets better as you gain levels.
There are lots more reasons but for a 'rookie' Regeneration is going to give you alot less pain as you start out than with other sets, and it's fairly constant as you progress in levels.
Now if you're going for a concept character, then all this goes out the window. My personal favorite secondary is Super Reflexes, it's the only 'natural' secondary out of the bunch, but it's a slow starter and takes some patience to get used to.
Basically, I would roll some test characters and test out all the secondaries and see which one suits you best.