u/Potss always has good advice, even if it's not dead on the mark for what you want.
I think you will be fine to get into the hobby with an inexpensive rifle, and later upgrade if you need the competitive edge. That said, if you start inexpensive, make sure there is a clean upgrade path. I don't know much about 3 gun, but I know that the A2 FSB (front sight / gas block combo) can make the rifle difficult to upgrade for accuracy later. Instead, you want to make sure you can easily incorporate a free float hand guard with a low profile gas block.
With this in mind, I would not recommend the Ruger AR-556 or S&W M&P Sport II rifles, as they are built around an A2 (style) FSB. The Aero OEM rifle at Brownell's is a good alternative start.
You have your choice of free float hand guards and can (easily!) later swap in a nicer 18" ARP barrel and adjustable gas block, etc.