Best all around hunting caliber is .280. imo
.280 is certainly a good all around round. I cant think of any good rifles chambered in it around $400 though. Maybe $600 and up.
But If we are talking about best all around hunting cartridge instead of a deer rifle around $400, I would say .270 and 7mm Rem Mag would possibly eek out the .280 based on availability and selection of ammo. Although any of the three would be appropriate for all around hunting in all the lower 48, and they all will do basically the same thing...if the hunter does his part.
I like the 30-30 though, as I typically hunt in the Florida brush. And it is also a good round for hog hunting. and the marlin 336 is a short light rifle that comes to shoulder fast. And with Hornandy's ammo, it really stretches the max distance before the round starts to tumble. Plus its a lever gun. Everyone should have one.
But mostly I recommended it because it was in his price range, and if he is going to be shooting further than 200 yards anyways, he is gonna have to invest some real money into a solid bolt action rifle with real glass(not cheap) attached. I would say the investment would be $800 minimum. And for someone just getting into the sport, that can be steep.
But YMMV.