Ahhh...the Trumpet...what a wonderful intrument. I've played the Trumpet for ten years now.
I would say go with the Bach Trumpet. If you want to buy cheap, then you'll be getting a crappy Trumpet. Having a good built Trumpet does help with your playing. You can start off with a Bach Gold trumpet, or just buy a silver bach one. I have a silver one.
In terms of mouth pieces, I think when you first buy it, it comes with a 7c mouthpiece. 7c mouthpieces are good for beginners, make sure you get that one. As you get better you can goto a 5c or 3c. The difference in numbers is the size of the mouthpiece hole. The lower the number the bigger the hole.
As for where to buy it, I'll have to look into that.
Buy a Silver Bach Trumpet if you want to spend the money.

The 300$ one is a good if you want to spend the money.