Bench with freeweights on a barbell. If you plan on competing you have to train that way. Given your SQ and DL numbers, you probably need to make sure your SQ is to legal depth. About 99% of the time when someone new to powerlifting has a SQ way higher that their DL it's due to squatting high.
I don't know if this is the case with you, but you should make sure. I would also recommend 5/3/1 for training since it is simple and has you doing the main lifts regularly. I would also recommend you learn to conventional DL. I think most beginers should learn this style first, then experiment with sumo later. In my experience the majority of lifters pull more conventional than sumo when pulling raw.
As for the grip, first make sure you are using an over-under grip and chalk. If you are having trouble holding on to 370, then almost any type of grip work will probably help. The most specific exercise is probably static holds in a power rack. Simply set the pins at a height that is a couple inches short of your DL lockout.
Using a double overhand grip pick up the bar and hold it for max time. When you can hold a weight for ~15-20 seconds or more then increase the weight.