I'll also recommend the T-Bolt as well. Mine is the Sporter version and has no problem keeping 1/2" groups at 50 yards with the bluing, checkering and fit being typical Browning quality. The Double Helix magazine is really a very cool design that's easy to load but pricey for extra ones. The drawback to it for some is it is lightweight (Varmint Model a little heavier) and the polymer trigger guard but neither one of these things bother me. The trigger is adjustable but mine only goes down to 3.5 lbs which is fine to me as well but may not be for everyone.
I also have a 504 that is an incredible shooter as well. Great styling and a heft to it that makes it feel like a "man's" rifle. The problem with these are there were some tooling issues with the barrels in the early serial numbers so they were very hit and miss in regards to accuracy. Remington corrected this by replacing the worn tooling later in production but the reputation was already established so this is why they no longer make the 504 which is a shame. Mine was an early model but it shoots the lights out and easily groups a 1/2" or less at 50 yards. The nice thing is they are cheap now and should you get a problem child, you can put a Lilja barrel on it or even a Shilen barrel and still be within your budget and have one hell of a shooter. Actually, the Remington 547 is the 504 action with a Shilen barrel along with stock upgrades that they command a premium for. The trigger on these are easily adjustable down to a very low poundage which is also a nice benefit. As far as the serial number thing goes, I've read anywhere from 5xxx or 6xxx on is good to go but I've also seen where it doesn't matter as it's all a crap shoot. Mine is in the 3xxx range and it's a keeper for sure and has enough strong features that it's worth a gamble in my book.
I've always heard good things about CZ's and they have quite the following. For me, their styling leaves a little to be desired and I think it's the way the magazine doesn't fit flush along with the shape of the trigger guard and trigger. Savage is the same way for me in regards to the magazine. For whatever reason this doesn't appeal to me but I'm funny like that. Still can't knock their reputation for accuracy though.
Another option would be a used Kimber or one of the Browning / Winchester 52 reproductions although they will be pushing the max in what you want to spend but well worth the money. The Weatherby XXII, which is now discontinued, features the Anschutz 64 action and most seem to be pleased with it's accuracy and it's absolutely stunning in my opinion although I do wish the magazine fit flush. Of course I've always been partial to Weatherby's stock style/design so I could overlook the magazine issue on this one LOL!
You've had a lot of good recommendations thus far and any will bring you all kinds of enjoyment. Personally, I'd opt for a more expensive model at this point since you have the money and treat yourself to it. Some of the lesser expensive guns would be easier to pick up down the road as let's face it, you can't have too many rimfires and variety is the spice of life!