How/where to cut this rose bush please?
In the house I moved in to in summer 2013, there is this rose. Between then and last autumn, I let it grow quite a lot, trailed it up a fence - but I have no idea how to keep a rose and it went horrible - so, in autumn/winter, I cut it right back, to the top of this green branch...

Since then, in the last few weeks, it has begun growing again, not from the green branch but from elsewhere. It looks like it really wants to grow strong from there. (That said, there are a couple of nodules starting on the other side of the green branch, too).
My question - should I cut the green branch off to let the lowest new shoots do their thing? Shall I also remove the rest of the redundant bark/branches?
Is there any risk of disease to exposed branch joints left behind after hacksawing/secaturring?
I aim to keep this bush much smaller and healthier this season.

Thanks for your help!
Posts
...there's no need to prune any more, you've done enough to it... you've got new shoots that are appearing on the green stem, and also on the brown woody stem right where a cut has been made previously, besides those lovely red ones at the base.... just feed in Spring and let it grow...
..if you make any more cuts now, at this time of year, it could let in bacterial canker.... there's just no need....
I agree with Salino, I use blood fish and bone in spring but you can get fertiliser especially for roses
I agree too. March is the classical month for rose pruning, but your rose is already fairly severely pruned so leave it. Is it a climber? You say you trailed it up a fence. If so then let it keep some long strong stems as a frame and when you prune just cut off weak shoots, very old and woody shoots and the side shoots growing from the main stems to two or 3 buds.
Make sure it doesn't dry out in summer, and feed it, I use rose fertiliser as it has the right minerals. Instructions are on the packet. Feed as growth starts in spring and again after flowering is the basic minimum. Roses are quite thirsty hungry plants. They also like being mulched with well rotted manure. A well fed rose is better able to fight disease.
Roses often get a bit tatty later in the season. Don't spray against insects, you will kill good insects too, but do spray with a fungicide against diseases like black spot, mildew and rust.