A premium potting mix is usually pretty good. Something with organics and goodies like mycorrhizae for root health. I also mix in a little pumice. Don't forget the names on the sides of the pots. The band ID plastics always seem to fade out on me.

Hi Michael! Welcome to roses!

Any good quality potting soil will work, with or without fertilizer and/or moisture crystals. It doesn't really matter as long as it's a good light weight, easily draining soil meant for pots. Never use garden soil or regular ground dirt because it's too heavy and will not drain well enough. Potted roses will need extra watering and fertilizing because they dry out quicker and nutrients get washed out quicker. So even if you buy the potting soil with fertilizer in it you have to feed them through the season anyway.

With the bands it is best to graduate them up in steps to bigger pots. So those 1 gallon pots are perfect. You would not want to put those tiny bands into the bigger 5 gallon buckets right away. Maybe next year though depending on how big they get.

Those 5 gallon buckets sound fine to start your bare roots in as long as you put in enough drainage holes. Bare roots are usually 1 year or older and larger in size then the bands to begin with. As the roses get larger you made need to put them in bigger pots though if it's going to be a while before you can plant them in the ground. For a full size mature (it takes about 3 years for a rose to mature) hybrid tea I go with 15 to 20 gallon pots. It will just depend on how long you have to keep them in the pots before you get your yard ready for them.