I have my climbing Explorer roses and clematis on concrete reinforcement mesh. It's only about $12 for 8' X 4' and will last many years provided you paint it first.

Mine is secured to the wall of our house with a couple of large hook, like the type used to hang cups in cabinets. It's been up since 2003 and hasn't rusted or bent.

I also have one for my raspberries which I secured to 2 rebars which act as posts on either end.

I find with my climbing Rose that allowing a distance from the wall of approx 12" - 14" to the rose A WOODEN trellis made from cedar 1 X 6 X 8'L fence board that is ripped with a saw to produce strips simply cut and nail this wall support together to form a sturdy upright and mount to a south wall with anchors.
You're not entwining the rose to the trellis. Your tying the main stems to the trellis 1x1 support using green garden string to keep it straight as it grows higher

Climbing roses require heavy duty trellis because these plants can be pretty heavy. You wouldn't want to have to replace that trellis every few years. Climbers are tied to the trellis. I wouldn't encourage anyone to put a climbing plant against a wooden wall because of mould and insect issues. Instead build a trellis as far from the wall as possible. Make sure there's a gap. In anycase with any roses, they need the air to be breezy to reduce mildew and black spots. You can make it very simple using 2 thick posts and using metal bars for cross beams. In fact these would look very modern.

As for choices of climbing roses.. do check out pickering nurseries online catalogue for suggestions. Climbers grow beyond 10 feet - maybe even 14 or more feet. Ramblers are another one that can be considered as climbers but they only grow to 9 feet or so. In a small space, a rambler may be more suitable.