ballistics of the 303 Brit and the 308 Win are pretty close. If you consider your rifle to be a decent shooter, the same ranges apply. Some fellows use the 308 Win out to 1000meters with good success.
It all depends on how well you've got your rifle shooting and how well you know it. It also depends on how well you can dope the wind and mirage at longer ranges. Some bullets have a tendency to drift into the twist at longer ranges as well. If you're going to shoot extreme ranges, you will have to invest in good bullets with concentric jacket thicknesses as well. Long range shooting is a whole different ball game, there are very many factors to take into account if you want to be successful.
There are many volumes written on long range shooting. Go to the ranges and matches that host the shoots and watch. Talk to a few of the shooters there. They will be only to happy to show you what's involved. They're always looking for new blood.
Just get one thing straight in your head though, once you get started on the accuracy trail, one inch groups just don't cut it anymore. You will never be satisfied with off the shelf rifles again. Some think this is BS but if you get really serious about it, you will always be pursuing that elusive combination that will give you a consistant one holer. Learning to adjust the paralax on your scope can take up a couple of months. It changes with conditions and your particular eyesight.
I won't delve deeper into it. Figure out whether or not you're going to use micrometer adjustable iron sights or AO adjustable scopes.
I won't even get into triggers. $$$$$$$$$$$$$$$$$$$$$ is a good place to start. If your $$$$$$$$$$$$$$$ are in short supply, stick with what you have and be happy with it. I know a few fellows that buy a dozen match barrels at a pop. They high grade the batch when it comes in and flog the rest, usually for substantially less than they pay for them. It's darn tough to compete with someone that has this kind of $$$$$$$$$$$. It boils down to an equipment race in many cases. I have a 303 Brit that was built with a Shilen match grade barrel. It was contoured to look exactly like a military barrel, right down to the bayonet lugs and knox. It has a .308 bore, a tight chamber and headspace. The necks need to be turned to chamber the cartridge. It shoots like a dream. It's also glass and cork bedded. By the way, it's still chambered for 303 Brit, it just uses .308 diameter bullets, mainly because good bullets are easier to find.