[g.willikers]

You are speaking of Bullseye the competition, rather than Bullseye the reloading powder, yes?
If so, first check the rules for the matches you are thinking of attending before buying anything.
Local rules for any of the games can vary from the standard NRA Bullseye rule book.
And, of course, definitely get that and read it thoroughly.
If nothing else it shows the folks running the matches that you are serious enough to have done that.
As for choosing between irons and a dot sight, that can depend on the distances you will be shooting and your eyesight.
Also on if the matches are indoor or outdoors, as the target distances and lighting conditions can vary quite a bit depending.
In other words, first research the matches and then the equipment.
Attend a couple to watch and learn.