Conformation, temperament, athletic ability, record of acheivement, and a breed either matching or identical to your mare all need to come WAY above colour.
Not just for the stallion, but assess your mare too@ is she high enough quality to ensure her baby is going to have a worthwhile role in the world and will get a home? The exception should be if you can guaruntee the foal a home for life.
There are five 'paint' patterns you could look for: tobiano, frame, sabino, splash and rabicano.
With all of them except tobiano, there is a very high chance the pattern will express so minimally you may not even get a 'painted' horse.
Frame and Splash can cause blue eyes. Some people like them and some don't.
GET YOUR MARE TESTED FOR FRAME. Just because she looks solid doesn't mean she couldn't have it. If your mare is heterozygous for frame, breeding her to a stallion who is also heterozygous for frame has a 25% chance of resulting in LWOS. All responsible breeders test their horses for frame if there is even the slightest chance they have it. Many owners of studs do not get them tested, so if you do not test your mare, you could be taking the chance that both carry frame. The best paint breeders (and therefore probably those with the best stallions) will always have had them tested for frame. Ask to see official test results, too, because people lie.
If you test, and know for sure your mare does not carry frame, then you may breed her to a stallion carrying it without risk. However, the foal from this has a 50% chance of becoming a carrier, meaning IT should never be bred with another carrier.