marlin 30-30

If you are going for deer only and can use a rifle, as others have said, a Marlin 336 is the route I'd go. Here in Iowa we can't use centerfire, so I have a Benelli Nova 12ga combo deer/smoothbore as well as a Knight Disc Extreme 50cal ML which gives me deer and pheasant hunting from Sep to Jan.

If you want to get a rifle take a look at something in 30-06 ( I personally like Savage).
The muzzleloader does not give you any real advantages at the ranges you said you would be shooting so the only reason I would get that is to extend your season. So if that is your goal then go for it.
If you want to get a shotgun take a look at an Ithaca 37. You should be able to easily get 3" groups at 100 yards with their old smoothbore "slug" barrel, and you can always get another barrel with interchangeable chokes for it.

in miss. where i hunt, they let us substitute some older larger cal. breach rifles for prim. weapon (muzz) hunting. Purchased a 45-70 by NE firearms last year. It's a hunk of lead, but seams like it would be great for woods hunting (under 100 yrds) after that the bullet falls from the sky. If NC has no prolonged muzz. loader hunting season, i'd stay with cartridge rifle. 30-06 is a great all round gun, just in case a longer shot presents itself.

WHEN YOU COMBINE DEER AND ELEPHANTS, YOU GET BARAK OBAMA.(:
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i hunted with with a marlin 30-30 with a bushnell 3-9x40 scope the only reason i stopped hunting with it cause it was my grandpa's and wanted to retire itand get something a can varmit hunt anddeer hunt with. You can get a new marlin 30-30 around $375

REM 870 12gaComboOR MOSS 835 Combo

I'm with Rebel Hog on this one. Probably the most bang for your buck would be something like the Rem 870 combo. It will give you the deer gun that you want since, as you stated, most of your shots will be 50-75 yards. Plus you will still have the use of a regular shotgun, which if you buy the 870, is very dependable and will last you a lifetime. You also stated that you are buying for 3. Someday if you wish to get a more expensive shotgun, say a browning BPS, you will have the 870 to pass down to one of your little ones.

Another vote for a lever action 30/30. I'd say Marlin first.

I have a Savage 111 Combo in .270 and it has been a great deer gun. Got it for less than $400 and can shoot 1.5" groups with factory loads, so it it plenty accurate. If you want to later on you can add a nice scope and have a real shooter.

I would also look at a shotgun two barrel combo. You can add a scope with a rifled barrel and shoot out to well over 100 yards with the right ammo.

Good luck with your decision.