You know, Chris, I'm not an expert on this topic, but I've read a great many articles and heard a lot of testimonies about how accurate bolt-action guns are. Frankly, I don't know first-hand because of all the guns I've ever owned, for some reason I've never owned a bolt-action gun.
I'm mostly into pumps and single-shot guns.
So, while the word seems to be that Bolt-actions are best, I would not trade my 40 year old Remington 30.06 pump for any other gun.....period.
Single shots are also fun and they force you to take your time and make the best possible shot, since it may well be the only shot you get. That puts something of a challenge on the shooter.
Get whatever you feel comfortable with and then shoot that sucker every time you can until you are driving tacks with it......then you will be ready for the hunt.
It isn't what happens to us, it is how we deal with it, that matters most.