Well, there are a huge number of rifles that can legitimately be called Enfields- ranging from Civil War muzzleloaders up thru the heyday of the British Empire, to the 1960s. A good start would be some reading- and this is one of a million bits of info- http://en.wikipedia.org/wiki/Lee-Enfield
USUALLY people are referring the the SMLE or the No.4 Mk1, or the Jungle Carbine.
First, if you do not know the gun, know the seller. (Thinking of getting that as a tattoo)
Next, skip the Jungle Carbine. There are more fakes than real things. If you find the real thing, they had a problem called "wandering Zero"- accuracy sucks, recoil and muzzle flash are..... interesting.
The SMLE is from early 1900s up into WW2. The No4 Mk 1 is from about 1943 on- and all other things being equal, the No 4 will likely be in better shape. The No 4 has much better sights, and has changeable numbered bolt heads.
Design of the bolt results in headspace becoming greater as rifle wears. The No 4 has either 4 or 5 (can't recall which) bolt heads. If you have a 2 bolt head, and cartridge cases are stretching when fired, you can replace with a 3 bolt head, and you are good for another 10 years of so.
Check to see what bolt head is in the rifle (little number stamped on the bolt head)- If it is a 4, getting to end of easy fixes,( now time for gunsmith fix) and check condition of bore (corrosive primed ammo) and condition of muzzle wear (GENTLY insert point of a .303 cartridge into muzzle- should stop before brass gets to muzzle)
Avoid rifles that have been "sporterized" unless they are cheap and that is what you want- collector value died when they were butchered.
We have some folks around here that are die hard SMLE fans- they will be by directly. An errors above should be corrected- will not hurt my feelings, and were due to age and a couple of glasses of wine with dinner. I am NOT an Enfield expert- have a few I enjoy shooting.
No 4 Mk1