Never thought of Remington 760 as front heavy.
Any rifle with a tubular mag under the barrel gets front heavy when loaded to capacity.
Bolt guns can typically handle high pressure big bore cartridges better than semis or lever guns. While there are exceptions (50 cal semi autos) you won't see an 'African hunting round' like .416 Remington or .375 H&H in anything but a bolt gun. People TEND to take their eye off target or at least point the rifle down when cycling a bolt gun.. that's a training issue that can be cured. Bolt guns remain the most accurate of the platforms.
There are flanged (rimmed) versions of those big African rounds made for double rifles, which are by far the fastest way to get two accurate shots with a heavy caliber downrange.
Pump guns just aren't that common anymore but at the turn of the century many US makers had a centerfire pump action rifle intended for hunting. I suspect Winchester bowed out of pump guns in favor of 'magnum' rounds that were becoming available post war. Remember pre-war a lot of guns were made in a labor intensive process. It's possible that it simply wasn't economical to make them 'the way they used to'.
Remington remains the last hold out making pump rifles in numbers .. however as someone pointed out it works EXACTLY the same as an 870 shotgun, and can be had in .30-06, .270 and .308.. arguably the most popular hunting calibers in North America. They are pretty accurate rifles as well as being almost as fast as a semi auto for a practical aimed follow up shot.
Lever guns were some of the first successful attempts at creating a repeating rifle in the USA and for that reason alone remain iconic. By the turn of the century the lever gun was being offered in pistol calibers like 38-40 and heavy calibers like 405 Winchester (which had a ressurection of late). The lever gun remains "THE" deer rifle most hunters over 50 grew up with, be it a Marlin or a Winchester. It was the icon of the cowboy era, the silver screen westerns and but to amazing use by trick shooters like Annie Oakly. They are mechanically more complex than a bolt or pump gun, but they are pretty robust. Follow up shots are fast and there's really no reason to take your eye off target when cycling the action. The flat profile of the lever gun makes it easy to store behind a truck seat or in a scabbard for those that still ride horses.
Semi autos can get lead downrange in a hurry and may have a high capacity magazine option, but until recently a precision semi auto hunting rifle was a high priced endevor. It's only been in the past 20 years or so that the AR platform has been 'pushed' to new rounds like 300 Blackout, 458 socom, etc. Most AR-10s right out of the box out shoot FAL's and M-1a's and even Remington's 742.
Any one of them will put meat on the table, anyone of them COULD defend your life in a pinch. It's pretty obvious a bolt action rifle is a poor choice for home defense but the best choice for long range shooting. The lever gun soldiers on while only one manufacturer still makes a pump action centerfire rifle. Semi autos abound now as the most popular rifle type in the USA, though not many people actually hunt big game with them. (revised for clarity)
Whatever you choose, try them all.