Best thing to do is go to a good school like Sankey Rodeo School for your first several horses. Get on as many as you can at the school. Sankey will have all the equipment you need other than boots which they can recommend the right kind of boots. Call them if you have any questions on what to take, and they will cover all of the equipment in great detail at the school.
Ideally you would get on your first 30-50 at schools and clinics put on by professionals. The reason this is important is the combination of being around professionals who have done it at the highest level and being matched to the right caliber of stock.
Expect it all to be kind of a blackout or blur for at least 25 or so head of horses, so there isn't much point getting on anything that really bucks. By 100 or so you'll be at that stage where you have practiced the mechanics enough at home and have been on enough horses that you will be somewhat conscious of what the horse is doing so you can actually ride something that bucks for real.
The good thing about being 21 is that you don't have the injuries of someone who started young does, and you don't have any bad habits yet. The bad is that a roughstock career is pretty short, and you need to be in the best shape you possibly can at all times. If you are still riding in your mid 30s you'll be the old man, so make it count while you can and good luck!
I’ll echo what @jgnmoose said. I started at 19 or 20. But I was already in the military and my rodeo career was sporadic and brief.
I did find that I was being out scored by the guys who had been at it since high school. There were no schools back then that I knew of, so you have that advantage. With that comes the opportunity to ride an assortment of horses. I had only what I drew in the competitions.
What I did get from it was an appreciation for stirrup leathers that give me good freedom of movement. Also I got a good sense of balance and for reading garden variety knot heads that I find myself on from time to time.
Funny, but before I decided to be a team roper (header), I was seriously thinking of being a saddle or bareback bronc rider. This was in 1986 and I was 37 years old.
I knew a guy who had his PRCA Permit in saddle bronc. I was over at this house one day, told him my thoughts about being a bronc rider and he got one of his ropes. Showed me how to form a loop and swing it. After watching me, he said "save your body and try for team roping. For not having any lessons, you swing a loop very good."
So, bought a descent rope horse, tack and a Rattler brand heading rope. Went to a roping school a guy I knew put on, started going to jackpots and, next thing I knew, I bought my PRCA Permit for team roping/heading. To save money, I borrowed a trailer and, on weekends only, was headed to local rodeos.
At the age of 37, that definitely wasn't the age to think about being a bronc rider. That is for sure.