Known as the Smelly (or SMLE) for Short, Magazine, Lee-Enfield, aka the No.1 Mark III, was the standard rifle of the British and Commonwealth nations from 1907 into WW 2. Possibly the best battle rifle ever built.
Yours probably has GR inscribed on the band at the wrist- all arms were property of the crown- stands for George Rex.
Info for you- Collecting and Shooting the Enfield No. 1 Mk III - HISTORY
Value of any gun is based on exact make, model, condition and originality. Thus the spread in price JP just gave you. These ARE subject to excessive headspace due to wear, and should be checked by a smith before shooting.
Caliber .303 Enfield, aka .303 Brit. Moderate recoil, with soft point ammo, capable of taking about any animal you will find in America with possible exception of BIG bear, Sasquatch, and whales.