I will try break it down for you,I hope you take my advise the way I intend it.
From what you write, you have never owned a rifle and from what I understand you have not shot one either or have no experience with them.
So here is some method to my madness. Recoil between the 308 and 30-06 can be a jump up for the novice shooter. There is nothing a 30-06 can kill better than a 308 if shot placement is correct and premium ammo is used,this is right up to Eland. As a new shooter/hunter a 308 will serve you well for many,many years. Nothing wrong with a 30-06 and the war between the choice of the two calibers is just as old as the war between supporters of the 9,3x62 and the 375H&H. It boils down to couple feet per second,grains and grams. I will always choose the shortest cartridge that delivers on par performance (except for the Short Mags).
Working of the basis that you chose the 308 as your caliber,I will narrow it down by choosing calibere specific actions. Actions that have been designed or built around the caliber it will fire. CZ actions in the 308 and 30-06 range are the same,so is the action Musgrave use (VZ 24) a 308 round looks kind of lost in these actions as there is a lot of space between the tip of the bullet and the ramp. Under recoil the shorter bullets tend to move around a bit more in the magazine.
Tikka,Sako and Remington have calibre specific actions for their rifles. Whether it's a top fed or mag fed rifle makes little difference in the medium calibers,it's the magnum and DG calibers were I will only consider a top fed rifle.
For your first rifle I do suggest a wooden stock to add some weight and balance to the rifle. Just take care of the wood.
Forget about a Varmint/Sniper type rifle with heavy barrel etc,but a hunter class/type rifle. They are fine out to 300 meters which is way to far for you to shoot as a new shooter/hunter anyway.
Choose a scope to match, a 3-9x42 is more scope than you initially need,but enough to use for many,many years. Get the scope mounted as low as possible on the rifle.
Do not get a rifle with a Hogsback style stock,stick with a straight stock.
Forget about a rifle that is guaranteed to shoot half inch groups, a rifle that shoots 1 inch groups is more accurate than you can shoot from field positions anyway.
The last consideration is after market parts and factory warranty. Remington and Tikka probably have the greatest selection of aftermarket parts available.
If you choose a 308 take a Tikka in 30-06 a CZ is fine.
My best suggestion is not regarding the rifles,go and find a gunshop or training centre or pay a reputable Hunter/Shooter to take you to the range and teach you a few things about rifles and safety. That is the best investment you can make in yourself and your hunting/shooting future.
Best of luck.