Mark the ones you like, and research as much as you can.
Is it fragrant? Is it hardy? Remember, climbers can easily be pegged to the ground (or into pots) for airlayering, then you can snip them off and have more plants to give away to friends so that's a plus too (also, if you wish to cover a huge wall with one you can air layer it and plant the babies.)
What size is it? Are you aiming at having pretty bushes in pots to bring in as centerpieces occasionally? If so, make sure you have a SMALL bush size. Minis are all different. Some sprawl, some reach up several feet, some are teeny bushes like Si. Some are thorny and some (like Cinderella) are not. The HelpMeFindRoses site is invaluable for this.
http://www.helpmefind.com/rose/roses.php?tab=5
This is the advance search page.
Look at your John's Mini catalog, then look up ones you like. You may be surprised to find some qualities not listed in the catalog (it is odd but I have found out a catalog will leave out positive info on a plant sometimes, in the interest of brevity in the copy. For instance, in the Tiny Petals site there was no mention of the fact that Grace Seward has an intoxicating fragrance. NONE, nor do I remember the Cinderella listing as saying it had no thorns (it does not have any.)
You may also want to restrict yourself on colors; the Dropped Bag Of Candy school of garden decor has its fans but you might not be one of them so think about it NOW and not later. It is a little late when you have ten bushes roaring rainbows at passersby to decide you really wanted a subltle line of pinks and not ORANGE then PURPLE MAGENTA then YELLOW GOLD then.... I'm getting grief from relatives for that sin.
Oh, and for giving away the Red Cascade. I thought, no scent, it's gone...well, it is missed. Drat.

KribbyKat,
I don't know of a good white climber. If you can't find one, try Red Cascade or Work of Art. I have the former and have heard the latter is wonderful, but I've nowhere to put it.

I absolutely adore Hot Tamale and its sport Ruby Baby. John's has Ruby Baby listed. Gorgeous form, nice robust bush. The scentsational series is great for fragrance and not without substance for flower or bush. The Sunblaze series is good for robust garden color, but aren't exhibition contenders except for the 'garden mini' classes, where available. (If exhibiting is of any importance, of course).

Glowing Amber, Starina and Incognito are very nice. I'm sure most of the rest are prefectly wonderful, too, but those I have experience with. I have others from them, but they are still tiny and haven't bloomed much yet.

Suz

In the back pages of John's catalog, they list Climbing Snowfall.

Pandora is a nice creamy white, but not a climber.

Here is a link that might be useful: Pandora at Help Me Find