Alsatian

A bolt action rifle with a scope would be a natural choice, unless your circumstances are special (deer rifle for close-in brush hunting might rather lend itself to a short barreled lever action rifle, for example). A .340 Weatherby may be a bit much gun for even a full-grown, experienced adult shooter. Am I understanding you to say you have borrowed this rifle and shoot it and can use it for target practice -- say a box of 20 rounds or more per trip to the rifle range? If you are not a mature shooter, it is probably advisable to start with a milder cartridge and migrate to more powerful cartridges as you mature as a shooter. The danger of shooting powerful rifles too young is that one may develop a flinch rather than a controlled trigger pull. Of course, in individual cases mileage may vary.

Along the lines of milder cartridges, in order of increasing recoil:
.243: good for varmints, antelope, and deer
.25-06: good for varmints, antelope, deer, and perhaps sheep. More powerful than the .243.
.270: good for antelope, deer, sheep, and in the minds of some people, marginally suitable for elk. More powerful than the .25-06
.30-06: good for antelope, deer, sheep, mountain goats, elk, moose. More powerful than the .270, perhaps not as flat shooting as the above three cartridges, but if you aren't shooting over 300 yards you probably won't notice the difference.

I think you might be well advised to select your first rifle from among these very popular cartridges, leaning towards the lighter end of the scale. You know, you can use a rifle for awhile and then sell it later for perhaps 1/2 of your new purchased price. If you buy a used rifle, you may be able to sell it later for the same price you paid for it. The point is, you are not marrying yourself to this rifle for life: it is not a "til death do us part" arrangement. There are other suitable cartridges, but they are not so popular and hence the ammo is not so readily available at any mom and pop store.

As far as rifles themselves, the Remington Model 700 and Winchester Model 70 have many adherents. Ruger and Savage also make quality rifles, and perhaps are less expensive.

Try to buy a quality scope, as a low quality scope may betray you in a critical situation and cause to your missing a precious opportunity in the field. Again, you may wish to consider purchasing a used scope.

Provide more information about your needs and others or myself may provide further advice.