Ramblers put out long, pliable stems and have only one flush of flowers a year - climbers have stiffer stems and are usually repeat flowering. There is also a pruning difference - ramblers need pruning around September, whereas climbers can be left to do their own thing, though sometimes a bit of judicious pruning may be necessary to persuade them to go where you want them to, and later perhaps to remove any dead wood. Climbers often do not get as large as ramblers, so may not actually get big enough to climb high enough in a tree. The following roses are suitable for training into trees - Cecile Brunner, Climbing Francois Juranville, Rosa Filipes Kiftsgate and The Garland. Rosa Canary Bird, even though its classed as a shrub rose, will do the job too, but it flowers quite early (now) and then has no more.
If you want a more modern variety, check the height and spread it reaches to see if it will be suitable for your tree.

Paul's Himalayan Musk, also great for growing into a tree.

As Bamboo says, ramblers only flower once but they can put forward a fantastic display for a relatively short time. Climbers spread out their flowering over a repeat or longer, continuous season. One way to get over the all or not-a-lot would be to plant a rambler and a climber together.

As you want it to grow into the plum tree, pruning is probably not a major issue but you would need to keep an eye out for disease and de-tangling any dead wood at a height could be a challenge.

Thanks for responding, I will have to have a think about which one to choose but thanks for the suggestions.