You CAN build a lower cost rifle that is competitive with the high dollar brand names.
I would agree with the “barrel and trigger” majority for priority #1 and #2, but what has been largely ignored in these responses, and is a requisite to a very good shooting rifle, is the BEDDING. (Which is combined with free-floating of the barrel.)
A lot of guys buy a bunch of parts, bolt them together and expect precision. If you are at all handy, consider DIY bedding your receiver using an aluminum pillar and epoxy, or get someone that has done this before to help you. Two bedding points are not required if a single point is done properly. Pillar/epoxy bedding gives your system a solid, repeatable base that allows you to maximize the performance of that match grade barrel.
The rifle pictured has a “blem” laminate stock ($39.99), a stock Ruger receiver and bolt, a Kidd Match Grade bull barrel and Kidd two-stage trigger. (If you do not feel the need for an expensive “chassis” stock, you can save a bundle$$$.) The bolt has had the edges lightly smoothed with a belt sander to improve reliable function. The receiver has been bedded using a custom (self) made 5/8” diameter aluminum pillar and bedded with steel epoxy. Aluminum pillars are available online from several vendors. This rifle now wears a discontinued Athlon Helos 8-34X scope ($499) with a MIL reticle on a 20MOA base, and has a Picatinny rail bolted to the underside of the stock for quick bipod attachment.
Similar pillar/epoxy bedding on another 10/22.
Image is of 5-shot groups at 50 yards with three different lots of SK's excellent Long Range Match ammo.
(The '294', '314' and '321' numbers are abbreviated lot#'s, NOT groups sizes!)
I can’t remember exactly the total cost for the components, but certainly less than $800 (w/o scope). While not going to win any benchrest matches, this is more than adequate precision to compete with the high dollar brand name rifles in rimfire PRS/NRL22 matches.
EDIT Addition: Beware of using a thumbhole stock. When a PRS stage calls for shooting from your "support" side (if you are right eyed/handed, then you must use your left eye, shoulder trigger finger), holding an opposite contoured thumbhole rifle gets awkward.