I'm not at all familiar with what's 'new' out there now. But personally I'd ride along with just about all here and look around for a used MArlin 336 or a Winchester 94 in that caliber.
Both were made in a number of different versions. Differing bbl lengths, mag tube lengths, stock styles, sights, ect.
The Pre-Remington era Marlins seem to be in more demand as are the pre 64 mfg Winchesters.
All will do the job and it doesn't sound like you';re buying for collecting purposes, so look around with that in mind. A few beauty marks or some lost finish does not make the rifle any less useful in the woods.
With care it'll still look the same 50yrs from now as it does the day you bring it home.
Some of the trainload of Commemorative issues made by Winchester on the 94 were made in rifle configuration and with things like an octagon bbl and fancy wood.
Any of those that have been shot and/or used have no collector value and as such go begging for owners. Some good looking rifles among them. Some are a little too glitsy looking for some tastes!
These will be Post '64 mfg, 94 Winchesters so there again the collectors backed off from buying them.
Perfectly fine rifles for walking the woods though.
Another one you may run into is a Mossberg 472,,or you may have seen one and just past it by thinking it was a Marlin336 as they look very similar.
Made in the early to late 70's it was a decent rifle but nothing about it to really recommend it over the Marlin or Winchester. Some around with WesternAuto Revelation house brand marking on them too.
If a lever action is not your only option there were a few bolt action editions made over the years.
Remington Model 788.. These command a pretty good price as they have a record of excellent accuracy in this caliber
Savage Model 340..A utility grade bolt rifle also made in .222Rem.
...Don't loose the detachable box magazine in either of these..
Winchester made the Model 54 bolt rifle in 30-30. The 54 was the grandfather of the Model 70.
Not too awful difficult to find one in 30-30 but the usual source will be on-line. Prices more than the average L/A for sure.
Some other odd ones around like the Remington Lee Sporter, but your chances of running in to one of those is pretty slim. Buy it if you do though!