RE: What bows are the "big three"??
You really can't go wrong w/ most of the bows manufactured these days. Most of the hype and adverstisements are for Hoyt, Bowtec, & Mathews.
The PSE lines (PSE, AR, & Browning) are starting to get more publicity these days.
They are all very good bows. It should just come down to a personal preference... Look at the variety of different bows everyone replying to this post shoots.
I personally shoot a Mathews now, but have owned and liked Hoyt & Archery Research.