I also wanted a fun to shoot rifle that could produce better than average groups. I chose the savage 10fv and ended up with a smokin deal. I've been more than happy with mine. It was between a Remington 700 sps tactical and the 10fv. I will tell you that I never have liked how 'loose' some of the Remington actions feel, although I can't deny they are shooters. Just my machinist OCD coming out. The savage stock also ended up being a little better than the rubbery stock the sps comes with (the forend doesn't touch the barrel with a bipod for starters).
You might be able to get a used or lower end new Mini 14 for around what you're looking to spend. It's hard to go wrong with that, unless you just don't really care for an autoloader.
Do yourself a favor and just go purchase one of those ugly Savage rifles! another one I would look at would be a CZ. Granted the stocks on the Savage rifles are for a better term poo you can get another stock from several manufactures for about what you'll have in the Remington trigger to get it acceptable (sorry fella's I quit Remington years ago! I didn't want to spend the money to get things where I wanted them) want a different caliber? sure not a problem a couple of cheap tools and a new barrel go no go gages and 30 minutes later you have a 308! From a guy that loves to build rifles just get the Savage it'll make you smile I promise! Later,
A savage is hard to beat very accurate and pretty easy on the wallet. I have one and it is a shooter. I do all my coyote hunting with it. For a single shot a Ruger No 1 Varminter is pretty much top of the line in my eyes.