.303 British is a cartridge, not a name of a rifle.
The vast majority of rifles chambered in .303 British in the United States today (I'll assume you're in the USA) are some variation of the Short Magazine Lee-Enfield, which was the standard service rifle of Great Britain and its colonies- Canada, Australia, New Zealand, South Africa, India, etc.- for most of the 20th century, including both world wars. It's a safe assumption that your rifle is one of these.
http://en.wikipedia.org/wiki/Lee-Enfield
Early rifles were marked "SHT.M.L.E." or "S.M.L.E." on the receiver wrist in front of the buttstock and above the trigger guard. Some time after WWI, the Brits changed the designation system to numbers, with the No.1, No.4, and No.5 being the most common types. (No.1 corresponds to the original S.M.L.E. model.) The rifle number is followed by a "Mk" or mark number, which designates the sub-type, which is sometimes followed by an asterisk or "star" that indicates a further modification- e.g. No.1 Mk III* is spoken "number one mark three star."
FWIW the word "Short" does not refer to the magazine, but rather to the overall length of the entire rifle, to differentiate it from the longer initial model colloquially known as the "Long Lee".
Many, many surplus Lee-Enfields have been modified from their original military configuration- or "sporterized"- to better suit the desires of post-WWII American (and Canadian) hunters. The quality of such conversions varies widely, although it tends to be poor, as the rifles were once considered nearly worthless and were often modified in the owner's garage using hand tools. A fellow I met at a gun shop related the story of buying his first centerfire rifle- a surplus No.1- for $8 in 1962 out of a 55gal drum(!) at an East Dallas hardware store.
You can find loads of info about these guns on the Googles.
THAT SAID...
There are a
few .303 British rifles around that are NOT Lee-Enfields. These generally fall into 3 categories:
- The British Pattern 1914 rifle, a military bolt-action design roughly modeled after the Mauser 98 and used as the basis for the U.S. M1917. This rifle was originally intended to replace the Lee-Enfield, but this did not happen for various and sundry reasons. These are sometimes found sporterized.
- The Ross rifle, a straight-pull design designed and produced in Canada, and used as the standard Canadian battle rifle early in WWI until it was realized that various design flaws made it totally unsuitable for trench warfare. Most Ross rifles in circulation are military surplus, and are often found sporterized, but a handful of commercial Ross sporting rifles were sold here as well; these are generally quite valuable today.
- An American or British commercial bolt- or lever-action sporting rifle produced in the caliber, usually pre-WWII. The most common type is the Winchester Model 1895, but it's a stretch to describe these as "common"- more like "somewhat less rare". Compared to former Commonwealth military rifles, these are needles in the haystack.
