Tionese tanking set is definitely fine. You could probably do it in daily purples too, assuming competence and a good healer. My Vigilance alt does just fine in that spec wearing mostly-Columi gear (a bit of BH, BM, Rakata and WH too.) I mean, as long as you have 50% armor reduction and then about 20% defence and 30% shield and absorb that wouldn't present any issues at all. Just make sure you use Hyper Fortitude stims to make things a little easier on your healer.)
Daily purples and purples you've purchased off the GTN should be fine for running the first three HM's. And if you know your healer you should be fine doing most Tier 1 HMs you encounter.