Any of the calibers listed will do fine. There are other things to consider before you choose.
Do you reload?
If you do, then that will somewhat negate the low cost advantage of the 30-30. If not, the cost and availability of 30-30 ammo puts it far ahead of the other calibers. You can find a staggering variety of 30-30 ammo and it is the cheapest by far to shoot if you only shoot factory loads.
The 35 Remington is one fine caliber and if you reload you can improve its performance somewhat.
The 44 mag packs a whallop but you will be limited to 100 yard shots. Good ammo availabilty though; many bullet choices make it a good pick especially if you alresdy own a revolver so chambered as well.
The 444 definately packs the mail but it was designed around pistol bullets so it cannot fully live up to its potential for the reloader. Factory ammo is not widely available and very pricey.
Now the KING; the 45-70 Govt. This round is very versatile and can bring to bag any big game animal that walks earth and many that live in other galaxies I'm sure! If you reload, there are a wide array of bullet weights and designs that will handle any situation from the Barnes 250 grain FNX to 500+ grain cast and copper bullets that will bust the engine block of a cement mixer. Standard 300 grain hollow points are pure poison on deer.
There are other fine lever action cartridges for the adventuresome hunter too. The 38-55, 375 Win, 405 Win, 44-40 WCF, 32 Win Special, and my favorite, the 348 Winchester in the beautifil model 71 rifle.