Need advice on pruning some [very?] old roses

[Ms108]

I just moved in to a new house with what looks like very old, maybe poorly cared for, roses. I've never grown roses before, so my questions are: what should I do with the unpruned rose, and did I prune the other one correctly?

I uploaded pictures to an album here: https://imgur.com/a/beSPx

Thanks!

[tomc]

Keep up on mulch. it helps reduce water needs, and serves as low-N fertilizer.

Rose are the swine of a garden. They want the most sun, fertilizer, and water.

As your eyes travel to the soil-line note if there is a knobby part. That is the union between top and root wood. If you prune away everything above the graft the root-stock will be all that grows. And it will very likely not be the same as the scion was.

Pruning back to lively wood is a good idea.

[imafan26]

Use very clean cutting tools. Spray them with alcohol and make sure the blades are sharp. I use loppers on thicker canes.
Cut out the dead canes. Depending on where you live. You should prune roses to the 5 strongest canes in a vase shape. Cut just above and outward facing bud and leave about 8-10 inches of the cane. Mulch for winter. Feed roses when they break. After each bloom cycle they should be fed. Cut back tips to a a 5 leaflet node and chose nodes that face outward. You don't want branches growing in because they will cross and rub and can cause injury to let diseases in. The rose in the picture looks like it was cared for properly. The canes are thick and were cut back at some time.