If you're new to both and looking for an inexpensive way to start shooting, a Lee Enfield is a great choice for a starting rifle. That said, if you're brand new in general, you might consider getting an inexpensive, bolt action .22 to build up your shooting skills.
As mentioned, .303 British is chambered by a handful of rifles, some expensive, most not. Its an older, military cartridge that originally used black powder. An entry level gun to look for would be a Lee Enfield, either No. 1 Mk3 (WW1 Vintage - with some exceptions) or a No4. Mk1/2 (WW2 and after vintage) which has been 'sporterized', meaning that much of the wooden stock has been cut away to reduce the weight of the rifle. Googling 'Sporterized Enfield' will give you some examples. These are common as mud anywhere in Canada and represent possibly the most used rifle/calibre for hunting in our nation, at least historically. You can expect to pay anywhere from $80-200 for a sporter.
Things to consider: The sights on the No1 Mk3 are different from those of the No4. Mk1 - the former uses a notched 'ladder', where your aim is to put the front sight blade between two posts - and have your target sit immediately above those aligned points. On the latter, there is (usually) a peep sight, adjustable for range, through which you look, placing the top of the front sight blade in the center of the circle made by the peep, then putting that blade on target. This is also good because the peep is set at the rear of the receiver (unlike the ladder which is forward of the receiver), giving you a longer 'sight radius', which contributes to greater accuracy. Some prefer one style over the other, I prefer a peep, as I believe it to be more intuitive and accurate.
When you're getting your first beater Enfield, for gods sake dont do what I did. Check the bore; different rifles will have a different number of grooves, depending on the mindset of the manufacturer. Usually it'll be 2 or 5, though there are variations. The number of these grooves isnt quite so important as their depth and the overall state of the bore. If it has been 'shot out' - the grooves will be shallow and hence wont give the bullet alot of spin. Likewise, stay away from bores that are pitted, overly dirty or frosted. There's enough Enfields out there that you can be picky.
If you've got money to burn, go buy something expensive, others here can tell you about them.
Enjoy!