You could go to a big box store like Lowes and find one you like and that will survive your indoors environment. Read the tag for the plant's light, temperature and moisture requirements and find a match that seems to fit the space where you plan to grow it. Have fun!

Joseph

Generally, it's harder, and the results are less positive, to try to cheat by getting outdoor perennials going sooner because they are exposed to unnatural conditions, or at least unnaturally-timed conditions. The starting indoors to get a head-start thing is usually for annual plants that may not have time to complete their cycle if started from seed outside later, or who's blooming cycle can be greatly extended by doing so.

Most Clematis don't bloom all summer, many bloom only once for a few weeks. Causing one to start blooming sooner than it would outside likely won't cause it to bloom for a longer period, but could get you another flush of later blooms on some.

Good point above about the roots of Clematis preferring to stay cool.

A morning glory or moonflower vine might benefit much more from being started inside early, happy in a pot as long as it's a big one. That kind of vine will continue blooming indefinitely, until it gets too cold. A Mandevilla would also be OK with being in a hot pot, and bloom for a long time.

There are house plant vines you could enjoy inside all year, if that appeals to you.