Anything chambered in .204 Ruger, .223, .220 swift, .22/250 will do the job you are asking for. Then, if you want to get fancy and seriously long distance you could go with a custom 6mmRem AI pushing an 87grain V-Max at around 3700fps or a .243 loaded up with a 58grain V-Max smoking out there at 3900+fps (same bullet 6mm but different case).

Actually, if you want a good rifle caliber/cartridge that you could get factory loads for and use it for Varmint as well as whitetail, it's pretty hard to beat a .243. 58 grain for varmint and 80-100 grain load for whitetail.

Now if you are a reloader, your options open up significantly. But since you don't feel you will be shooting past 400 I won't bombard you with those.

As far as being a lefty, your bolt action options are limited but if you want a good semi like an AR pattern rifle you can get all of those previously mentioned cartridges in either a AR15 or AR10- (LR308) platform and you can get ambidextrous controls. I shoot left and right handed rifle and the ejected case never hits me in the face nor does it disturb my sight line when shooting lefty. I did a brief search and found a few good lefty bolt actions with Ruger, Savage, and Remington but it seemed a little salty price wise in comparison to the right handed models. But I guess that's probably par for the course.

Also, don't skimp on glass. Glass will either make or break your shots.