I second everything that appyt posted. IMHO, whether a horse readily accepts the transition from snaffle to curb greatly depends on how it's introduced.
I love browsing Amazon
's bit selection, they have thousands, some of which are awesome and I really want to try them and others make you cringe, but they've got a bigger selection than any other online store. I don't know about anyone else but I've never had any luck finding anything I liked in an actual tack store. They tend to either have the really cheap crappy bits or super harsh bits and I don't want either of those types.
Here are a few good bits that are starter bits for a horse just moving up from a snaffle. While you're deciding what bit you want to try, get your horse started on learning to neck rein well if he doesn't already. The transition will go a lot smoother if he already has at least the basics of that down. And, realistically, from a training standpoint, you shouldn't even attempt to transition up until
he neck reins decently.
And here is another link to the one that appyt pictured above (which I also use and like a lot)
I also really like the looks of this bit and plan to buy one soon to try it. I know that another member here, Cowchick77 really likes the square ported bits like this.