You have a lovely carnosa! I like to refer to them as the "OG" carnosa or "heirloom" carnosa. These have been around for a long time, shared by many, and will continue to give and give.

Carnosas can be happy in many types of media. They dislike having wet feet. So whichever media you choose, just be sure to let it dry completely before watering again. I like to grow my carnosas in a chunky mix. But rest assured that many people have grown them potting soil for decades.

Fertilizing is one of those other opinion type things. I give mine DynaGro Foliage Pro. But the woman I got one of my huge carnosas from used tomato fertilizer on hers and they were gorgeous. You can also use foliar feed sprays like orchid spray. Don't over think it. Just give it some food but don't over feed.

They like to climb or trail. They will put out long vines that will initially be leafless and those will want to wrap around something. They will literally wrap around themselves or anything in their path. They wrap counter-clockwise. So if you do give it something to climb and give it a headstart, be sure to remember that.

If you want a bushier plant, you can chop some of those vines and root them in water, then stick them back in the same pot.

Just to give you an idea of their potential, here's the one I inherited from a neighbor before I brought it home. Yes, that's one pot.

this is the "tomato fertilizer" one too.