Tom,
I started with my "old 270" a couple years back, myself. So, I'll chime in.
I'll start off with the basics you need to shoot further.
A. An accurate rifle and load. You can take your one hundred yard group size and multiply by the yardage you're shooting to get a best case group size. For example, if your rifle and load shoot 1/2" groups at 100 yards they could produce 5" groups at 1000 yards. If the rifle shoots 2" groups at one hundred yards it could shoot 20" groups at 1000. This is oversimplified, but you get the idea of the importance of an accurate load and rifle.
On your old Remmy you'd want to at least bed the action (making sure your barrel is free-floating), and tune the trigger. The rifle may or may not be accurate enough after this. But, these steps are easy and inexpensive.
B. A scope with accurate tracking and nice knobs. An adjustable objective or side focus is extremely helpful also. A couple exambles of the less expensive ones are Nikon Monarchs or Buckmasters, and the Bushnell Elite series. Good power ranges are 2.5-10, 4-12, 4.5-14, 4-16, 6.5-20.
C. A good rangefinder. I think the best buy goes to Lieca. Others are Newcon and Bushnell. Remember to look at the ranging performance on various surfaces. The advertised yardage capability is often grossly exagerated. There are reviews of any you might like, on here.
D. A way to measure slope. There are little dials that attach to your rifles, some rangefinders measure incline, and simple pendulum type cards you sight over.
E. Finally, you need accurate drop and drift data for the load you're shooting. There are ballistic programs in the bullets, barrels, and ballistics section. You'll need to go over the input section. Then you can research each input field you don't understand. Data needs to be tested. Some folks carry a pda so they can enter current conditions for more accurate drop / drift data. Others carry cards. I carry a card that unfolds like a paper doll. It fits under the ammo sleeve on my stock. The first page is a "standard conditions" graph. Consecutive pages contain correction data for the variables. I may start carrying a pda as well. All drop data needs to be tested. There is a learning curve involved in producing accurate drop data.
Now, I'll address your questions.
1. Opinions vary. Some say 1000ftlbs others 600... On big game I would give the 270 an effective range of 800-1000 yards, depending on elevation, size of animal, shot angle... My rifle and load seems to be quite consistent to about 800 yards. My percentage for good shot placement seems to fall off after that.
2. Power range is really a matter of preference. You could certainly kill big game at 1k with a 3-9x. Personally, I like my rifles to be versatile. I like a 4-16. I carry the rifle on 4x. The 16x really helps when shooting small targets (milk jugs or prarie dogs at 1k) and for proper bullet placement. I actually have all of the power ranges mentioned above on various hunting rifles. The Nikon buckmaster 4.5-14 is a great, versatile, inexpensive scope.
3. By factory I'm guessing you mean you don't handload. I think it will be difficult to get the kind of accuracy and consistency you need with factory ammo. There may be match type factory ammo for the 270. A good place to check would be Midwayusa.com. For bullets you want High Ballistic Coeficient (B.C.) bullets. These bullets have pointy tips and boat tails. You also want a bullet constructed for hunting. Sierra, Berger, Nosler, and Hornady are popular. I shoot 140 grain Hornady sst's and Nosler 140 grain accubonds in my 270.
4. Already covered
5. I'll address a few.
MOA stands for minute of angle. 1/60th of one degree. Imagine a wedge. The wedge widens as it gets further away from you. 1 moa = 1.047 inches at 100 yards, x2= 2.094" at 200 yards, x3 = 3.141" at 300 yards...
We talk about MOA in two contexts. First is relating to group size. I might say, "My rifle and load will shoot 1/2 MOA if I do my part". This means the rifle will shoot about 1/2" groups at 100 yards and 5 1/14" groups at 1000 yards if I shoot perfectly.
The second is relating to drop and wind drift correction. If I set up for a 1000 yard shot with my 270, I will enter my data. Zero,100 yards, Temp= 50, ellevation=5000', humidity=10%, pressure 24.52, line of sight angle (incline)=10 degrees, wind speed 2mph, wind direction, full value- from 3 o clock . My ballistics program will then tell me my drop and wind drift corrections in MOA.
My 270 load drops 270 inches at 1000 yards under these conditions. To obtain a MOA correction the program would divide the inches of drop by 1.047x hundreds of yards. In this case, 10.
270 inches divided by 10.47 = 25.78 MOA I would then turn my elevation knob up 25 and 3/4 MOA to compensate for bullet drop. This would allow me to hold the crosshairs on the target. Next I would turn my correction for wind drift. In this case it would be about 10" or 1 MOA to the right.
The important thing to know is wether your program and scope are using MOA ,1.047" per hundred yards, or simply inches (1.0)per hundred yards. For example your ballistic program may state a MOA correction of 25.78. If your scope adjusted in inches rather than MOA your 25 and 3/4 correction would only correct for 257.5", resulting in a miss 19" low. Just make sure your program and scope are the same. And they each do what they say.
A minute is short for minute of angle. We might look at a 3" group at 600 yards and say, "That's a half minute group, sweet"!
A click is a division of MOA or Inches per hundred yards. Most scopes have click values of 1/4 Moa. Your knobs will be marked like a ruler. Each MOA will have three 1/4 MOA hash marks. As you turn the knob they click over each mark. Hence we call them clicks. So if I want to turn my elevation knob to correct for a 5.5 MOA drop I would turn up to the five, then two more clicks.
Some scopes have 1/8 adjustments, others have full 1MOA per click. The most common and most useful is 1/4.
Drift, or windage, relates to horizontal bullet drift due to wind. Estimating and correcting for wind is perhaps the trickiest factor in long range hunting. Shawns article on the home page would be a great source of info.
Good luck, and have fun!