Hmmmm well, most good tack stores will let you take a saddle on loan for a week to see if it fits/works for you.......atleast where I am they do
A barrel saddle is very specific to that discipline, you may find if you wanted to do another discipline that you might have a hard time moving around in it they way you need too.
A reining saddle (my favorite) has a low horn (so it doesn't get in the way of your reins) an open seat and a low cantle so you can sit back in the slides. I like these saddles because I don't feel boxed in.....also the fenders swing nicely on them so you can move freely.....(I think these saddles are pretty versatile, you can cut in them, you can trail ride etc.....)
A cutting saddle, similar to a reining saddle, has a higher horn (so ya can hold on!) and a lot of them have an open seat with a squared of cantle in the back.
A trail saddle, usually has a padded seat and a high cantle.
A roping saddle, has a lower, solid thick horn, mid-open seat.
I've never sat in a pleasure saddle......so someone else might come along and tell you about it!!!