"I live in the UK and use a .243 for deer. It is based on the 1908 Mauser (I think)"
Glad someone is still hunting in the UK! That ban on fox-hunting with dogs is terrible. .243 is a necked down .308, I believe. 6mm is a necked down 7mm Mauser, a similar cartridge, both great deer guns. 7x57, Remington 700 Mtn. Rifle is what I use for whitetails, it's a nice classic round that has plenty of wallop, but is not overgunned. I've shot plenty of deer with the old "thuddy-thuddy", but it lacks the energy to consistently knock them down fast. Plus with tube feed magazines, you're limited to blunt nose bullets. Faster the cartridge, the more hydrostatic shock, which equals faster knockdown on thin skinned, small boned animals like whitetail. (Although you don't want to go too small caliber.) Anything over 150 yards is pretty dicey with a .30.30. If you have any potential at longer range, I'd think twice. Plus, Marlin lever actions are hit and miss on accuracy. The one I had for a while was a dog. But the Winchester model 94 we have is pretty accurate for a lever action.
I also like the "old school" aspect of the .30.30, particularly if it's a "beater" rifle, that goes camping with you, maybe just has a peep sight (no optics to break), etc.
I wouldn't buy a new Marlin .30.30, but if you find a used one and your heart's set on it, give it a whirl. Try to shoot it first, though, as it may have been sold because it was inaccurate.
On the plus side, lever action guns with hammers are safer I think for a 15 year old. Something about pulling a hammer back to really make you think before the gun can go off. Using a shorter range, less powerful cartridge when young will also teach better shot selection later in life, which is always good. The .300 mag crowd for whitetails can be a bit much.