Its pretty hard to beat a 6mm for an all around deer round. The .243 is the classic survivor of the American 6's, it has even been adopted in Europe. A 270 Winchester may be the better all around round, but recoil becomes an issue w/heavier bullets/lighter rifles. However, since you already own one, that might simplify the cartridge availability issue/concern some.

In an American bolt action, as to brand it is hard to beat a Remington 700 for accuracy & readily available accessories, the Winchester pre-64 model 70's are as classic American as one is likely to find or utilize as an action base and the Ruger 77 flat bolts are known to have been very good more modern American rifles w/later iterations also performing very well.
If you want a small production bolt action classic, look for a Remington C grade from their custom shop. Those rifles had it all, hand fit & finish, custom stock, etc. Winchester had their Super Grades, but today you should expect to pay more, sometimes much more, for one of them.
For inexpensive & accurate, the Remington model 788's all shot very well and had super triggers & bbls right out of the box. Prices have gone up, but not rediculously so.

For scopes, a fixed 4X is plenty for deer hunting, I don't care what anyone says to the contrary. Have and use a good pair of glasses for glassing. I find a heavy 'post' to be a very useful reticle, but a standard cross wire works well also. Modern 'duplex' reticles are simply heavy posts with fine wires in the center, but they are cluttered compared to the single post type.

I will cast a vote for an older Marlin 336 with the Ballard rifling as being the better American classic lever action and as Ramiey says the 30-30 is a great choice in cartridges .. keep it inside 150 yards because of trajectory, but a good lever can put five shots inside 1.5" at 100 yards off a bench w/decent iron sights. The Marlins do not need extra holes drilled & tapped to mount a good receiver sight.

My suggeston is to bring your son in on it now; let him tell you his pref in rifle type and provide him with enough written info from other sources to make an informed decision on the cartridge choice. Tons of literature exists, much of it based on real feild information & observations too. His second choice when he becomes a bit older/bigger/wiser will be even closer to the mark of what he likes, but this first run will have significant value beyond mere action & caliber choices. He may even get a rifle that serves all his needs for a lifetime of deer sized and under use.

The Ruger #1's are fine single shot rifles, but they tend to be a bit heavy. Many of the older ones had spectacular wood. If you go that way, a 7x57 while a non-American round makes for a good all round cartridge choice.

Idle thots, post Thanksgiving dinner ... & nap :-)

edit: If you wish him exposed to 'Classic', buy a copy of Michael's book and let him learn some of what Michael has gleaned in a lifetime of pursuit.