Most of the time you can just hold on center. The bullet isn't going to rise or fall all that much. But, to answer your question, on most big game cartridges you would hold high on a close shot if you centered your rifle in at 100 yards. The reason for this is, the bullet actually drops before it starts to rise. It is kinda like a well hit drive of a golf ball. If you watch it close enough, you will see it actually drop some before it starts to get some loft. This is the reason most golf tees are built on mounds and not level with the fairway. If you sight your rifle in at 100 yards, chances are it hasn't even started to drop yet. At 125 yards or so, it may even be a little high. At 50 yards it will be around an inch or so low. I have shot the same rifle now for over 15 years. It is a 7MM Mag and I know how it shoots from 10 yards to over 500 yards. I have all the confidence in the world with this gun. Generally, where I hunt, if I can see it, I can kill it!
Actually, the bullet doesn't "drop before it rises" or even rise for that sake. A bullet fired from a gun begins its decent to earth and "drops" the second it leaves the barrel. The only drop or rise you think you see is the deviation of the bullet's arc from the line of sight through the scope. This arc will cross the line of sight through the scope twice. Somewhere around 25 to 50 yards and again way out depending on your extended range zero. If you're zeroed at 100 yards, don't ever hold high at close range. The most your bullet can be below zero at very close range is the height of your scope above your bore. Normally that's 2.5 to 3 inches max at the muzzle and moves toward zero at that 25 to 50 point. That's well within the kill area of a deer's vitals. I swiped a photo to explain.
As for .30-06 at close range. I've killed my share of deer with the 06. Took most with 165 grain Sierra Gamekings. I had one fragment a bunch through a front shoulder quartering towards shot. Killed the deer quick but that was the last I used of those rounds. Now I shoot Barnes TSX. I recovered one a couple years ago. Put a second bullet in a doe after she took the first bullet from my partner. Quartering away over 250 yards by a bit. Entered just behind the diaphram, raked both lungs, went past her shoulder, up the neck, and lodged just under the hide in her neck. Was mostly intact missing a couple petals. Quality performance in my book and she went down like a ton of bricks.
For the short range shots 150, 165, 180 grain doesn't matter. The construction of the bullet makes the difference. Some brands the 180's may hold together better, but put in the vitals they are all swift killers. Don't make the mistake of thinking one will always out perform the other because there's too many other factors involved. Just land it where it should go and that's all you can do.