Side view

View before winter stole the green....

I am not a pro or avid rose gardener, but I will give you my two cents anyway.
For the climber rose, Horizontal canes encourages more laterals, which produces more flowers. So you want to think horizontal in training the main canes.
If you don't like the Lattice trellis, you could install 4 to 5 medium/heavy gauge wires running horizontally every 12" apart along the wall. Then, train the main canes on them. They will shoot out vertical laterals and will be full of blooms in the peak season.
I have not tried this myself, but I think I would do it this way.

If you have not already done so, watch the video in this link or search "Paul Zimmerman training a rose on Trellis". He also have other videos for rose caring, pruning and training. Must watch for a rose beginner.

Good luck with the roses and post back how you did it finally!

Here is a link that might be useful: How to train a rose on trellis

As Rose Mom said, the more sideways you can spread the canes the more bloom you'll get. So you want to anchor the wires horizontally across that wall to have enough places to tie up the canes to. They look well cared for and healthy so you should get a lovely display!

Your house looks so inviting.

I agree. Place those wires horizontally. The canes look supple so guide the ones you can. The ones that want to be vertical can be tied to the wire in the fashion they wish to grow. Then as you study the overall effect at bloom time you can decide if any need to be removed. How exciting!

Have you decided what to use underneath? Guess you need to wait to see what color the roses are.