Need some ideas - school me

[86ace]

I am looking to buy that "one rifle" that gives me the best value and accuracy for my money. I just retired and have the money to spend, so I want to get this right the first time. Here are the criteria:
Purpose: groundhogs, coyote, and targets.
Expected range: For groundhogs and coyotes, generally no more than 300 yards with an outside chance at 400. Targets out to 500.
Caliber: I'm not a reloader, so looking for factory ammo. Was thinking .204 Ruger, .223, or .243 Win. I think all of these are suitable for my purposes, but I don't want to buy a rifle I can't find ammo for.
Scope: I've pretty much decided on a Zeiss V4, so that will be approx. $1,000 of the equation.
Budget: Between $2,000 and $2,500.
I want a nice bolt-action rifle, with a proper twist and barrel length, that will be as accurate as I can get. Prefer stainless. Thinking fluted and threaded barrel for muzzle brake.
Will be shooting with a bipod and generally not carrying on long walks.
I hope I have been adequate in my description of the criteria, if there are things I'm not considering let me know.
Fill me with some of your accumulated wisdom and experience, what am I looking for?

 

[Rick Richard]

That is a tough one because ammo is just about extinct. However, for a non reloader and what you have listed and the purpose I would go with the .223.

 

[nmbarta]

groundhogs= high volume shooting most of the time.
Rick Richard has it right on this one. .223 is very capable of 500 yard shooting
The Tikka t3x stainless varmint would be a good choice, though you would have to have the barrel threaded (no big deal)
1:8 twist should handle pretty much anything you want.
I would expect to this to be close to a 1/2" rifle with the right factory ammo, and would be surprised to not get a true 1/2" rifle with hand loads.
I'd look for some 69-77gr ammo, but wouldn't pass on anything in this market.

 

[Frog4aday]

What @Rick Richard Rand @nmbarta said. They nailed it: .223 Rem in Tikka T3x