Before you buy anything
A few things worth knowing first
Shoot 6.5 Creedmoor. Not .308, not 6mm Creedmoor, not .300 Win Mag. The 6.5 CM is the de facto PRS competition standard: excellent factory match ammo (Hornady ELD Match, Federal Gold Medal) available everywhere, manageable recoil, and proven ballistics past 1,000 yards. You'll find more competition data, more community knowledge, and more load recipes around 6.5 CM than anything else. Pick a different caliber after you've competed for a full season.
Buy your rifle from a local FFL dealer, not Amazon. Firearms can't be sold direct-to-consumer online without an FFL transfer. The Ruger Precision Rifle in 6.5 Creedmoor is the de facto PRS starter ($1,200-1,500 street price): chassis-style, modular, and the most community support in the sport. The Savage 110 Precision ($800-1,000) is a solid budget alternative with the excellent AccuTrigger. Find both at local gun shops, GunBroker, Brownells, or Cabela's.
Your scope budget should match your rifle budget. A $1,400 rifle under a $200 scope is a waste. The optic is where you see, hold, and adjust. The Vortex Viper PST Gen II at $550-650 is the right entry floor for PRS. You'll also need scope rings or a one-piece mount ($50-150), a separate required purchase people routinely forget to budget.
Resist the reloading rabbit hole for your first season. Factory Hornady ELD Match will get you through 12-18 months of competition with competitive results. Reloading saves money at volume and unlocks more precision later, but it's a second-year investment once you have the fundamentals down.