You do not mention what kind of rifle, nor what kind of ammo you can buy for 20 rounds for $17 - but anything that goes "bang" is likely better than having nothing.
So now you have a 308 Win. Do some reading, and figure out how to get into hand loading, sooner rather than later. Your hand loaded 308 Win safely and easily becomes a factory 30-06, mostly if bullet weights kept below 180 grains. Since the 1980's, our choice has been the Speer HotCor 165 grain bullet in the 308 Win - measured several time on Shooting Chrony, and others, as per the max loads given in Speer and other manuals - just so 2,800 fps - sometimes 10 or 15 fps more, sometimes 10 or 15 fps less over the years. At same time, if you can, chrony some factory 30-06 in the same weight bullets. Can also back off considerably and be nicely into 30/30 type loads - use the same bullets as used in a 30/30 - round nose 170 grain - at similar 2,100 to 2,200 fps velocity.
Was my reasoning why I picked 308 Win in a Win Model 70 as my first "store bought" deer rifle in late 1970's. Thought I had everything covered - likely did. By mid 1980's bought my second centerfire rifle, which I still have - another Model 70 but in 338 Win Mag - for "big bush up North" - for "bigger than deers" kind of animals. It was, and still is, a very useful pairing for almost all of us big game hunting folk. I took my first elk - a cow - with the 308 Win because it was only rifle that I had then; took several later with the 338 Win Mag. Our son has that 308 Win rifle - same deal - he took a spike elk with it - mostly because it was only rifle that he owned, then.
As far as "good for deer to 600 yards" do not know where that comes from? Very, very difficult to make a one shot kill at 600 yards - I have had a friend do it, with three others, but I was not there, when he pulled off that shot - I do know from other shooting with him that he could not dependably hit a round bale at that distance (5 feet diameter)- but that deer did a bit of circle after the shot and fell over - was dead by the time they got to it. More dependably, I think?? - most bullet makers design bullets to expand at minimum velocity of about 1,800 fps - so spend time in ballistics tables to find where your favourite drops down to that velocity - for most of us, is way hell and gone past the distance that we could hit with a cold barrel shot. And you can prove that to yourself - set up about 10" or 12" diameter gong or paper plates stapled to a lathe -is about the "kill zone size" on a deer - at whatever range - you get one shot - you hit or missed - your one cold barrel shot.
Perhaps a cynical comment about kill "distances" posted on Internet. Most of the prairies where I hunted are divided into 1/4 sections - so 1/2 mile to a side - 880 yards. Some areas have cross fencing into 40 acre pastures, so 440 yards fence line to fence line. In my buddy's case - so many paces from where he shot to this fence, across 40 acres pasture, then so many paces from that far fence to the deer on the ground. Any of us with rangefinders will tell you how viciously "wrong" many old timer "eye ball" ranging has been!!!!