I would check very carefully which stems are still alive (scrape a little bark off with a fingernail and if its brown its dead, if its green its alive) then cut off all the dead wood.
Don't let the compost dry out but take care not to overwater - wait until its almost dry before watering.
Black spot can be controlled by spraying the leaves regularly with a product called Roseclear - the instructions are on the bottle. If any infected leaves fall on the compost do remove them as black spot is a fungal infection and the spores will overwinter in the soil.

Most roses are usually much happier in the ground than in containers and they seem to do best in rather heavier soils so ordinary potting compost isn't the ideal medium for them, you'd be better with a soil based one like John Innes, so bear that in mind next time you repot. Once it gets going you'll probably be encouraged by how quickly it shoots up. Don't disturb it again though until the it goes dormant for the winter.

Hi, most roses are usually budded onto a briar root stock, which makes the desired rose more vigorous than if they're grown on their own roots, the advantage to having their own roots is that you wont get suckers, I agree with Steragram regarding everything else, Derek.