Don't own either a Savage or a Moss. (I own a Tikka), but I'll try to take a shot at what makes one bolt action rifle better than another. IMHO there are at least 4 things you need to look at in a bolt action rifle. The most important is the barrel, as this will probably have the greatest effect on accuracy. More $ gets you a better barrel. A top quality barrel will almost certainly be very accurate. Cheaper barrels will generally be less accurate and have more of a variation. You can luck out and get a pretty accurate cheap barrel. But a more expensive bolt gun/barrel mfg will consistently produce very accurate rifles. Some will give you a guarantee.
Actions - More money gets you a stronger, smoother, more reliable action. Once you have used a good quality action, it's hard to go back to a cheap one.
Stock - A more expensive/better rife will have a better stock. It will be stiffer/more comfortable/more adjustable, etc.
Trigger - a more expensive bolt gun will have a better trigger. It will be lighter, crisper and generally more adjustable than a cheaper trigger.
Having said that, although you can certainly spend $3-5,000 on a bolt gun, I do think you can buy a very nice bolt gun for under a $1,000. I picked up my Tikka T3X CTR for under $900. Savage and CZ also make some nice guns. Or you can pick up a Remington 700 for now, and then little by little upgrade and customize it.
Same is true of scopes. You can actually get some pretty decent scopes for $3-500. Of course you can also spend $2-3,000 on a scope. Additional money will get you spectacularly clear and bright optics, bullet proof ruggedness and reliability, and tons of adjustability to compensate for bullet drop out to 1000 yards and beyond.