A year ago I bought a used Marlin 30-30 for $300. Put a $170 Redfield scope on it and I love it. I used to hunt with my grandpas Remington 30-06 but I think it kicked more and was heavier. The 30-06 in my experience knocked deer down faster than the 30-30. The 30-30 bullet also seems to move slower and does more damage to the animal like a bigger exit wound in my experience.

Lots of possibilities here....FWIW my darlin' little wife is just a bit over 5ft tall (with a Louisiana temperment) and she shoots a Winchester Youth Model 70 in .308 loaded with 150gr factory ammo. Started her out on .308 and she never looked back.

I have a marlin 30-30 ZCenter point scope from wallmart $80 Love it with red and green lighted cross hairs



My sporter 1903 30/06 got this one for $243 at cabellas used rack

I know this will stir up a new controversy among the "ballistic technicians" here but I don't mind.
First, the notion that there is plenty of "30-06 out there".
So is plenty of cheap stocks. There is a very good reason for it. People are switching to more "comfortable to shoot" calibers.
The other suggestion about 115gr. or "reduced recoil" in 30-06 is pretty crappy to suggest to a beginer. 30-06 as any other caliber has a designated best BC and best sectional density in certain weight of the bullet. That is the one that gets the best ballistics. 115gr is a far cry from the 168gr that is close to a perfect marriage for this caliber.
There is very, very few 30-06 rifles out there that shoot real tight groups with a varmint loads at 150 yards, since very few barrels like them.
So the notion of recommending to a beginner to spend money on a gun that will not even come close to either .243Win or 25-06Rem in accuracy and wide ammo availability is beyond my comprehension.

You might try giving your location and maybe someone could meet you at a local range and you could find out for yourself what size rifle you will enjoy hunting with. My first rifle was a 270 and i still shoot it today. Also the recommendation to take the hunter safety class now is a very good idea and you will probably take a lot from it.