I'm in high school, and have played trumpet for 5 years. I want to learn all the brass instruments, and trombone is first on my radar. I want to know what would be good to begin with? I'm a sophomore, so what size mouthpiece should I use? Any special tips? What would be the average price for a good beginning trombone?

Yamaha YSL-354

By far the best student horn out there. Best craftsmanship, best price vs. quality. Some even keep those as a big band horn.

A good beginning trombone brand would be the Yamaha. For a reasonable price, get the Blessing brand. My first trombone was a blessing, and it very good. After school, I could afford a Yamaha. I noticed a difference, but the price difference was hideous.