So many ways to go, and this is gonna become brain overload, trust me....
My take, and just my thoughts for around $1k:
1) Out of the box and go compete rifle: Highly touted option is the Bergara B-14 HMR. Good rigid platform, decent starting trigger, chassis with flat bottomed front makes it easy for bag rests, slap a short pic rail in place of the stock bipod mounts, and probably invest in a decent $100 brake and off to the races you go. You can also pull the barreled action (2 screws...) and move it in to a KRG Bravo or any other higher end chassis down the road. The stock chassis it comes in goes used for around 300 so you can recoup a few bucks. The flexibility of this being a rem 700 platform gives a lot of flexibility from chassis to triggers for the future when you start thinking "upgrades" and believe me, that day will come. I know guys that competed with these for years and shot sub 1/2 MOA with their hand loads and certainly sub MOA out of the box with match ammo (per Bergara's sub MOA guarantee).
2) Tikka actions are the bomb but the default stocks aren't so much, especially for competition. In my opinion (and just an opinion) the CTR stock would probably be best, but again you can sell that stock for maybe 125 and drop the barreled action in to a KRG bravo (or other more expensive chassis) to give you some more accessory capability and even ability to add weight (which you'll want to do for comp). All in though this may be the most expensive option if you swap stocks. I'd say the Bergara barrels are a little nicer, given that's actually their core nitch, and the B14's barrel is a little heavier profile I believe (though shorter...).
3) The Howa Bravo, as mentioned above, is a good out of the box option as well. Really checks all the boxes and just need to add a brake. It comes stock in a KRG Bravo chassis and you can grab KRG accessories right from KRG as desired. You can actually save a hundred bucks by building it yourself though by buying the Bravo chassis direct from KRG and buy a Howa 24" barreled action straight from Brownells if you felt so inclined. Again, pretty much just a couple action screws. The Howa trigger is decent and can be lowered to a lighter pull weight with a little trickery.
4) The RPR is very popular and a good shooter. I'm just personally not a fan of the chassis, prefer open fore ends and Arca rails, and it doesn't leave a lot of room for change. It's always gonna be an RPR. I don't know a ton about the trigger either. Again, just a preference thing for me.
As for glass, you're gonna get hit with 300 options..... Be sure to leave budget for solid rings, or it's all for nothing. Leave 124-150 for decent rings (Seekins, Vortex precision, etc) and the rest for glass. On the "low end" I'm a fan of Athlon and an Ares ETR is a lot of optic for around $1k, and you can grab em here used for around 950. All I'll say, and again you'll get bunches of opinions on this, is I'd stick with something FFP, make sure it has a zero stop, MIL/MIL, some form of xmas tree reticle, and spend as much as you can afford.
