You forgot Canada for the .303 British. The .303 has been issued and in civilian hands on every piece of dirt on earth.
Let's start a different thread to discuss that if we'd like. We shouldn't get to far off topic of the OP's questions.
@ the OP,
I will give you a true story. I hunted my entire life with a 30-30 for deer. Killed the, killed more of them, and killed them some more. Some down where they lay and other (most all) run for some ways even if struck 100% best shot placement. Bullets have been recovered, and mushroom to .75 usually, but oh well. I still trusted in it, and then I found the 125 grain HPFN from Sierra. Absolutely turned the 30-30 into a drop them were they stand gun. I could get velocities out of the muzzle close to 2600 fps, and @ 150 yards it had some serious pop. Most shots thought were 80 yards and below, and more likely 35 yards down a pine lane out of a thicket. They work great. Not many shoot and track situations when you pop a deer with that bullet. 30-30 guys you all listening out there. Also I never found a bullet all were exits with great big holes.
Now a couple years ago the only place I had to setup was over a 300+ acre cow field watching tree lines, and a a couple old oaks out in the middle of it. Longest shot 300 some odd yards from my stand. Well the 30-30 just wasn't going to cut it that year. I had a 12 gauge, an AR-15, and a .303 British to use. The .303 was getting the call, but it is open sights, and didn't want to shoot that far without optics.
So I was in your exact shoes. Exact situation. I mustered up the money for a new rifle, and I would take the Bushnell 1.5-4.5x32 off one of my 30-30s and put it on whatever rifle I could afford. So I went to the local wholesale gun store "Academy Sports". I kinda had my mind set on a 7mm-08, but only had $300.00 to spend. I thought I could get a Marlin XS7 for $279+Tax. Well they had a special on the Marlin bolt guns for $249.00. I asked for a 7mm-08. The guy said, No. Dang... He said I have a .270. I don't like the .270. Don't know why just doesn't appeal.
Asked the guy what he had in short action Marlin bolt. He said .243. Nope. .243 Doesn't appeal to me either.
As I was walking away he said, WAIT sir! I have a .25-06. I called my BIL and said, look. I have a choice of .243 or .25-06. Same price, but I don't know much about the .25-06. He said, buy it now before somebody else does. You will not be disappointed. So I hurried to the counter, and snatched it up.
I put the Bushnell 3200 1.5-4.5x32 on it, and we sighted the gun in. I used 115 grain Winchester Supreme Ballistic Tips. Ended up killing two deer at the same time (two shots) with that rifle measured with GPS to 298 yards. I have since killed other deer, and every one have never taken another step. Bang/Flops.
My story is to just say that at 200+ yards you will have enough to drop the animal at that distance. Even farther.. But at shorter distance you will have more than enough to drop the deer. Get the gun that allows for clean kills at the farthest distance you could shoot. In this case 200+ yards. Which calls for the .308 IMO. Yes, a 30-30 will rainbow to 200+ yards, but you will have less than 1000 lbs of energy when the bullet hits the deer. Something to think about. I made the right choice, and I had plenty of meat that year.
Don't usually post articles by Chuck Hawks, but this will get you a pretty good comparison @ 200 yards.
http://www.chuckhawks.com/rifle_ballistics_table.htm