You need to learn what kinds of matches are held within whatever distance you would travel to attend. Ideally, you would find a match where you are able to dial your scope for each target or target set you engage. Unfortunately, PRS-style matches will present targets at varying distances out to 300 yards and require fast, precise elevation changes or holdovers for which your Tasco scope just isn't built. It appears that your scope has capped, field-style turrets which are intended to be set once and left alone.
Check the
NRL22 site. I don't know much about their matches because none are held near where I live (while other monthly or quartery matches are).
Here's a thought for you - find a match that's within a convenient distance and contact the match director. Tell him (almost always a him) you're a young, new shooter who is just getting started and you're concerned whether your gear would work well enough for the match. The expectation I have, based on the people I know who run matches here in NC, is you will be offered a rifle and assistance to shoot your first match. You are the future of the shooting sports, and experienced shooters want you to have a good time and learn while doing so.
In the meantime, you could check into the online training here. Click on your userid at the top right of the screen and select Account Upgrades. The selections have changed, but it looks like the "Supporter" upgrade for $20/month gets you access to the online training for tactical/practical shooting. So you go through all the training there, and then return to free membership.
There is a gold mine of information here in Snipers Hide. Overall, precision rifle quickly becomes a very, very expensive pursuit - even the rimfire disciplines / matches. You're young enough to have a lot of fun, and learn/practice the fundamental skills needed to shoot well, with the rig you have now. If your dad gets into shooting matches, that could be awesome for both of you. The main thing is to have fun. It's easy to lose sight of that when one gets "serious."
Good luck to you!