If it is a climber any cane that is draping towards the ground should be tied up so the end of the cane points upward. Make sure the trellis is anchored down as a high wind storm will take it and the bush for a ride.
I use twine to tie my roses up when they are young. Then I switch to number 22 black house wiring (you local hardware store should care it in spools.) That way I don’t have to keep re-tying them when the twine breaks. Of course that may be over kill since you only have one rose. I wouldn’t prune it until you find out what kind it is.
Q