If you want climbing roses, then you will need to put up either trellis or wire to support them. This will mean drilling into the brickwork/stone, but as long as the holes are drilled properly then it should not cause any damage to your house
Climbing roses might be preferable to rambling roses which only tend to bloom once a year - climbing roses bloom repeatedly through their flowering season.
Alternative climbers would be things such as Virginia Creeper (green leaves which turn a gorgeous dark red colour in the autumn) - these have tendrils which act like suckers attaching the plant to a wall, and so trellis / wire is not required. This doesn't cause damage to the brickwork but can be difficult to remove (we took off the Virginia Creeper when we moved into our house a year ago and you can still see the suckers on the wall). Ivy also supports itself, but the tendrils
can damage brickwork.
In short I don't think you would have any problems with a climbing rose!