I'm biased: I like and use my 9lb. Marlin 336 CB (Cowboy) 24" Octagon Barrel in 30-30. I reload, using a 170gr. Hard Cast Lead Gas-Checked bullet from Laser-Cast (a company in Baker City, Oregon) with 30 gr. of 3031 powder. about 2000fps. I don't use a scope, just iron sights. Marlin also made the 336 CB rifle in 38-55 Cal. (I don't own that one) but equally as popular.
Group size: if you do your part you could realize a minimum 1 moa group @100 supported. The fact is deer won't know the difference whether you shoot 1moa or more, as your "shot placement" is everything. Including shooting at an appropriate distance for the particular cartridge you choose, A quick clean kill is always what you want.
If your decide on a Marlin, look for a pre-remington made Marlin 336 marked on the left side of the barrel next to the receiver with a (JM) stamp. Even a Model 36 would do, which is just an older version pre-336. A (JM) Marlin 1894 45 colt, 44 mag., .357 mag. works too. Not to be left out the Marlin 1895.
With a Winchester 94 (1894 model)... I'd go for a Pre-1964 made Model 94 Rifle or Carbine in 30-30(30WCF), 25-35 WCF, 32 Winchester Special, 35 Remington, 38-55 WCF...better quality IMO.
You can't go wrong with a Savage 99 (1899) in 30-30WCF (Winchester Center Fire), or 300 Savage caliber is hard to beat IMO. The advantage of the Savage 99 is that you can use pointed bullets.
Have fun on your hunt and be safe.