From other posts, there seems to be some confusion between M1 and M1A. As far as I know, the M1 is the Garand. The M1A is a Springfield Armory trademark name for their semi-auto version of the M14. (Due to federal regs, the M14's can't be demilitarized -- once a full-auto, always a full-auto, regardless of parts swapping and who did it.)
Either will
work as a hunting rifle, though there are better choices.
For the Garand (which I know you didn't ask about), there are specially modified en-bloc loaders that hold only 5 rounds. For states that permit semi-auto rifles for deer hunting, but limit the number of rounds, this is usually a solution. Scope mounting on the Garand takes a variety of forms.
A rear mounted scope
must be offset, so that there is room for the en-bloc loader insertion. This requires (generally) a cheek pad to offset the head an appropriate amount to the L side. I've seen two styles of rear mounts. One is available from Fulton Armory and is described as a Griffin and Howe style (which is faithful to the WWII design, except for allowing modern 1" diameter scopes), and the other mounts in place of the rear sight. The Fulton Armory scoped version must be purchased from them - they don't install it on customer receivers. The rear sight replacement version does not require drilling and tapping the rifle, so resale value is preserved.
A forward mounted scope with long/intermediate eye relief can be mounted to a replacement rear handguard. This is a centerline mount; no offset. Generally, these can be mounted without drilling or tapping the rifle, which can ruin its value to others.
For the M1A, there might be a 5 round box magazine. I've never seen one. The scope mounts for the M1A are generally similar to the rear sight replacement versions for the Garand, except they are not offset.
As far as "touching 1000 yds", almost any modern centerfire rifle will shoot that far. Both the M14 and M1 were used in competition, because the military supported long-range competition. So, don't mistake .30-06 and .308 calibers with modern long-range benchrest competition. Those guys develop special rifles and special calibers to gain every possible advantage. The term "purpose-built" is sometimes encountered.
However, there are competitions that are limited intentionally, in the spirit of fair play and a level playing field. One of these is called a "JC Garand Match" and you have to shoot an essentially unmodified Garand with GI iron sights. Another is "F-Class T/R", and I believe either .223 or .308 caliber rifles can shoot at these matches. Scopes and bipods / front rests are OK. So, yes, you
can use a M1A (civilian version of M14) as both a range rifle and a hunting rifle.
Here's some pictures of a M1A and a closeup of a scope mount -
Here's a link to a current item on GunBroker showing bids at around $1000. The "buy now" price for this one is $1400. If you get lucky, you might get one for $1000.
http://www.gunbroker.com/Auction/ViewItem.asp?Item=105447942
Bear in mind that you can easily spend $400 trying to repair a used gun that has troubles. If you get one from Springfield Armory, they have a warranty.