When I built a 10/22 for long range shooting, I went with a Clark barrel and customized trigger. The barrel is a heavyweight bull barrel.
However, for steel challenge and other steel matches, those are shot at fairly short distances, under 50 yards and usually under 25 yards. For that, the standard tapered factory barrel is fine.
So my advice would be to stay with the factory barrel for the time being and put your money into these three things:
1. Lightweight stock.
2. A good target trigger. Kidd makes a good one, as does Volquartsen. I would opt for the latter because I knew old man Tom back in the day and he was a good guy. His kids run the biz now.
3. A red dot sight with a dot size at least 6MOA. For speed shooting, you want a big dot so you can pick it up quickly as you move the gun around. As you know, with steel it doesn't matter where you hit it, only that you hit it and it goes "ding".