Lady Banks Rose (aka the Tombstone (AZ) Rose).

Choose either white or yellow. Lots of threads here about it.

If you ever make it down to the Valley, both Berridges and Bakers have large selections of modern climbers for about $18.00 each, including several David Austin English roses that can be grown as climbers or large shrubs, like Teasing Georgie, Winchester Cathedral, Abraham Darby, etc.

One of my favorites is Climbing Iceberg which is just about impervious to the heat on the south side of my house. Climbing Night Owl and Sombreuil both get all-day sun as does Cecile Brunner. All are scented. Don Juan doesn't seem to like the south side of the house but CL America did. Both of these roses have the hybrid-tea style blooms and scent.