These are a few suggestions out of the many roses that grow well in the Desert Southwest. It's generally agreed that roses purchased at a retail nursery/garden center are superior to those at discount nurseries or chain stores.
There are excellent sources for roses on the internet, especially for roses on fortuniana rootstock, miniatures and old garden roses. Check out Rose Sources for suggestions.
Always select grade #1 bushes. Hybrid Tea and Miniature roses are probably the two most common types, but there are many other choices. Most types vary by flower shape/size, bush size/growth habit, bloom season and length of bloom. Roses are great mixed in the landscape, not just in their own beds.
Explore the possibilities! Check with local Consulting Rosarians for other suggestions.