Paperback is a general term which includes both mass-market paperbacks--that's the small ones about 4 inches by 7 inches--and trade paperbacks, about 7 by 10 or so. (There's some variation.) Mass market often cost about $6.99 or $7.99. Trade paperbacks cost more, usually $13.99 - $16.99. They're somewhat easier to read, with a larger font, bigger gutters, and more widely-spaced lines, and are usually on better-quality paper which won't yellow as quickly as mass-market paper, and made with better glue so the pages stay put.
Hardcover is better quality paper, and of course the hard cover which protects the pages. It's often no easier on the eyes than trade paperback, though, and it costs substantially more.
Since I'm not hard on books, I usually opt for trade paperback unless it's a book I'm sure I want to own indefinitely and will probably reread many times. Then I go for hardcover.