Don't waste your time. Move to Newport Rhode Island or the UK. They need lots of everything. Plant natives and you won';t have to do a thing. Rose's need to remain totally dormant for a period of time, battle rose bugs requiring tons of insecticide....... unless you plant a rose native to Kentucky.

I believe local climatic conditions have a great influence on which roses will do well. For example I grow a climbing rose called 'Royal Sunset' which thrives in my coastal California conditions but does not get a very high rating because it does poorly under so many other conditions. Roses do want some water so in a pot you'd have to see to it regularly .. well you would here but I understand that, unlike here, there are places wherre it rains between April and December.

You can absolutely grow them in pots, though they are generally more fragile then, prone to either drying out or waterlogging if the pot drainage holes come to be blocked, either by packed dense soil or by the roots themselves growing through the drainage holes and thickening over time. In pots, you have to water frequently and be careful with fertilizers, lest they become too concentrated in the confining space and chemical burn tender feeder roots.

Rose varieties vary a lot in mature plant size. The pot size needed depends on the variety. I generally used 16 to 18 inch diameter pots for minis or very young full size varieties and 20 to 24 inch pots for larger bushes. The largest pots are very difficult to move, so keep that in mind potted roses benefit from a repotting/partial change of soil every 3 or 4 years. Best done in dormant season or at late winter pruning time.

As for rose needs in general, pick varieties with healthy track records in your region. Some handle heat better, or extreme cold, or even both. Some prefer humidity, some relatively arid conditions. Some are more disease-resistant, some disease-prone.

Aside from full sun for six or more hours a day, roses like regular frequent watering, but roots cannot tolerate standing water for more than a day or two, so they also need good drainage. This can most reliably be facilitated with slightly raised beds, even 4 inches above surrounding land will make the crucial difference. They produce much better if nourished well, as they are heavy feeders, but pay us back by blooming over long seasons...the modern varieties, at any rate.

One really helpful online resource is helpmefind.com/roses, which is a great search reference tool, with descriptins and pictures and grower commentary on thousands of varieties, not to mention links on where to purchase.

A second resource is gardenweb.com, the sublink on roses. This is a chat site for gardeners and a great place to find many testimonials on specific varietes and attributes and quirks that describe them, as well as rose horticulture advice.

I've had a couple in containers and they did well (my containers were very large) but I found it easier to have then in the ground with mulch. I tend to go to the beach in the summer and my house sitter is not the best with plant watering....
Tips: do not water in the evenings if possible - you want the leaves to stay dry over night. Water well, especially the first year. Feed regularly. Watch for aphids & black spot.

I would suggest the smallest be a 12 gallon, and i say that without knowing the size you have pictured.