Chris,
Welcome to the forum and competitive shooting. Your question will generate as many answers as there are forum members here. Many members have custom rifles and tend to lean that way with our answers.
You didn't specify whether you want to shoot midrange, long range or both F-class events. Midrange is 300, 500, 600 yards while long range is 1000 yards. I have ran an F-class league for 6 years, getting new shooters into the sport. Many of us started as OTC shooters and used those rifles to start with. It has been quite a learning curve. I highly recommend you find a mentor to help you down this path, maybe someone who has a rifle you can borrow or use to determine of the sport fits your personality before you spend a bunch of money on it. My club has a starter rifle we loan out and I have a couple rifles on loan with friends who are starting out.
Eventually you will reload your own ammo so plan accordingly. Reloading is a huge part of the sport.
If you are going to shoot just midrange, I recommend you buy an flat top AR-15 with a 24-26" 1-8" barrel. The .223 is easy to shoot for everyone (don't let your wife shoot or you will be buying two of everything), good ammo is available (Federal Gold Medal or Black Hills 77 gr). If you already have an AR, even better, just get the upper. You can get by with a Harris type bipod or go with the Sinclair F-class. Many shooters use the AR as a learning tool and get to the point where they are shooting Master level scores with the rifles. That is about what an AR is capable of, generally speaking. Look at Rock River Arms and White Oak Precision for starters.
I bought a couple of the Savage F-class rifles when they first came out. Many shooter still start out and continue ot use them. For about $1200, they are amazingly accurate at times. Some will curse the triggers, others curse the barrels, but for the price, they really are amazing starter rifles right out of the box. Aftermarket barrels are available and easy to swap. Again for mid range, get the .223 F-TR rifle and have fun. The other option would be the 6mmBR rifle in the F-open configuration. Low recoil, easy to load for, but factory ammo is nearly impossible to find. The 6mmBr will get to 1000 yards so that is something to consider. The other Savage F-TR rifle in .308 would work too for both mid and long ranges, ammo is available and eventually to reload for. The Savage F-TR is a slower twist barrel so it won't shoot the real heavy bullets. The 6.5-284 is an amazing cartridge but it eats barrels and you don't need it for starting out.
Remington rifles are sort of the industry standard and the aftermarket is geared that way. You could get a Remington 700 in .308 and upgrade trigger, stock, etc as time allows. You would have a great platform for truing and future customizing. The fastest twist they make in a .223 is 1-9" I believe so you wouldn't be able to shoot the 80 gr bullets. Again, for midrange and starting out, that would be an acceptable compromise.
Most clubs that have leagues will allow darn near any safe rifle to be used. We don't weigh rifles, nor follow the F-TR/Open designations too much for starters. We just want shooters to have a good time and learn.
The classified ads here are a great start for what is available. Don't disregard a used rifle as an option. One more time, eventually you will reload so keep that in mind when you make your decisions.
Good Luck,
Scott