I am finishing up overhauling an early 80s bike. As the previous posters mentioned common shop tools work well. I used most of the following: hex and box wrenches, channel locks, ball peen hammer, rubber mallet, and lineman's pliers (side cut for housings). I didn't touch the headset, but everything else was touched.

I did buy two cone wrenches, as there are not too many alternative ways to snugging down the cone nuts. I didn't buy the freewheel removal tool, which I wish that I would have. I managed to find an old lug nut that just engaged the inside of the freewheel. It's not pretty, but it works.

My first experience in overhauling a bike was pretty much flying by the seat of my pants. Taking things apart and cleaning for the sake of doing it. A bike stand would have been fantastic to have. So, in the future for me a work stand and freewheel removal tool and all will be good until I find another tool that I need.

Edit: Thanks to the poster before me for the reminder. I need a spoke wrench. It is now added to the list.

Good luck.