TMC has always had a decent reputation as a place to start. Britton Transport has a finishing program too. Really small company with only one flatbed trainer though. Britton also has a more restricTed hiring area than the other recommendations you've gotten.
Melton and TMC I would also recommend but I know there are a number of anti-TMC members here but I think a lot has to do with where your home region is. Been a while since I was at TMC so I'm sure things have changed for the better and/or the worse so I can't speak from recent experience. If you can make a good hand at TMC for a year, you can punch your ticket anywhere given they are still highly respected by other carriers it seems. TMC will not tolerate sub-standard performance and will train right. But so will most of the other outfits like Melton and Roehl and BTC