It is going to be hard to get a 2 x 112 or 212 cab(s) for that great little head on your budget.
Two solutions IMO for a small rig:
1) Get a good quality 112 cab now, and eventually add another one when you have more cash. For this solution, I'd look for a used Bergantino AE112, or possibly consider a new GK Ne0112II (very reasonable, and quite good). Both have a nice aggressive voicing to bring out the mid complexity of that nice head. A used Aguilar DB112 (with the option of a second down the road) would be killer also with that head.
2) Get a good quality 210, which should give you about 75% of the performance of a 2 x 112 stack, and be loud enough with the TH350 to do moderate volume gigs. A used Bergantino HS or AE 210 would probably be within your budget. The TC RS210 is a VERY nice sounding 210 and would be in your price range new.
I'm loving my TH350 with my Bergantino AE210... tight, punchy, loud, and lots of midrange character. It won't rattle the rafters down low, but slots itself in a mix wonderfully, and is shockingly loud given the 175 watts into 8ohms rating of that head.
IMO!
Edit: The used Bag End suggestion is also a good one. Nice, efficient (if heavy) cabs that work well with the TH heads.