To tell you the best bolt action rifle I first would need to know what are you going to use it for, hunting, target shooting, sniper type shooting, competition, or just every day plinking?
And what cal. are you looking for & what price range.
There are some real accurate rifles out there, but what good is an accurate rifle if you can't afford to buy ammo for it.
I have seen guys buy a big cal. rifle, almost go bankrupt to buy ammo, only to be able to shoot a round or two each trip to the range because there shoulder wouldn't take it.
The best rifle would be a blend of what you want, what you can afford, where can you shoot it, what ammo you can afford to get, and most of all your knowledge of shooting.
Jake, I picked up a Sako a couple years ago and love that rifle. If you are looking don't rule them or Tika out. They are owned by Beretta. I had my heart set on a Browning A-Bolt when I found the Sako and haven't regretted buying it one day.
Remington 700 because if you want to over time upgrade it, more aftermarket parts, for lesser prices ,are made for it than any other rifle. I have a Remington 700 in 300 Win. Mag. which has been modified for 1000 yard target. However am going to a Short action in .260 Rem. for this endevour. Basically a necked down .308 Win. to a 6.5 mm bullet. It has very similar exterior ballistic characteristicts to the 300 Win. Mag. I would suggest a rifle in 308 Win. caliber to get started. It's a good all around caliber and can reach out to 1000 yards for target. Ammunition is also plentiful with a very good selection of various types commonly available.
Not a chain saw. My rifle is a 7mm mag Husqvarna. Well built, comfortable to shoot and a round that can be used for any size game. Had the gunsmith set the trigger pull for 3 1/4 pounds. Extremely accurate at all ranges.
On the other hand, using a big bore rifle for target shooting and plinking in general is not such a good idea. Ammo is relatively expensive and lots of high powered shooting is tough on your body, shoulders and ears. A better way is to work out a way to acquire 2 rifles. Nothing beats a .22 for plinking. A small caliber varmite rifle, .223, is a good choice for target and small game. Careful shopping and acceptance of used equipment should allow you to have both within the budget you have indicated.
You say you want to target and hunt with it but you didn't say how big of a game are you wanting to hunt?
Take a look at a Savage 110 or the 111 FCNS too, it comes in a huge array of load selection just pick the one you like. A 30-06 is probably the best all around hunting load and it's very popular in America but has a pretty good recoil to it. And since your wife will be shooting consider getting a better recoil pad then stock no matter the size of ammo you go with, it will make it more pleasant for the wife. It's not the prettiest of guns but it was built to be used a lot and can take a beating and still fire. You can get the package deal at Walmart for about $325, not including a better recoil pad, well under your price. The difference by the way between a 110 and a 111 is that the 111 had a external detachable magazine while the 110 is internal and thus not detachable. I would get the 111 because at the end of a day of shooting you can drop the mag, whereas with the 110 you have to cycle through all the remaining bullets to unload...BUT...some people are forgetful, they'll leave their home and forget the magazine thus for them a hinged floorplate (internal) mag is better. Really there isn't any need to get a more expensive gun, I can out shoot most much more expensive guns with my 111, so getting a $800 gun will buy you nothing other then better looks. Of course that's just my opinion and with guns everyone has a different opinion.
But I recommend you go to a gun store that has an indoor range and have your wife shoot a bolt action rifle in various calipers and see which one she likes before you jump in and get one only to find out she can't fire it.
I would save your money and get the Savage because you're going to need money for ammo and ammo today is expensive.