Unless you add some kind of supports, then you may want some vines that self-attach to the brick wall.

Also, evergreen and perennial are two different terms that you mentioned in your post. There are many more options for perennial flowering vines than evergreen flowering vines, but either way, you can usually find them pretty easily also at the local stores or nurseries.

In the Clematis forum, there are people who have successfully mixed flowering roses (including vine roses) with the clematis flowering vines. The effect is really nice.

Speaking of that, for the wall of the garage, it may be possible to use evergreen bushes if the space allows. Bushes and vines are definitely a possibility, with the vines using the bushes as a natural support.

Here is a link that might be useful: Try this

Welcome to Houston, Roselee! I am northwest of Houston (between Tomball and Waller) so we would have similar growing conditions, although we get a couple of degrees cooler in the winter than those in the city.

I have had excellent results using star jasmine (Trachelospermum jasminoides). It is an evergreen vine that will perform well in shade, or sun. It does not tendril, so you don't have to worry about it attaching to a brick wall and damaging it. The blooms are very fragrant and the vine is always healthy. This winter has been quite cold, but my vine never lost its leaves. I highly recommend it.
Molly

Molly, I'm still in San Antonio although Houston sounds appealing garden wise -- more tropical plants -- yum yum! I just moved a Houstonian's post over from the exchanges page. Thanks for all the suggestions for those folks. Keep them coming.

Roselee, I didn't read your post properly and I thought you moved to Houston. lol
Molly