Depends if you you want a player, or a period correct drum. Parts are interchangeable for a player. Serial number would be needed for a period correct drum.
60's drum "generally" had
1. Bottom rim with screwed on gates for early 60's. Later Fullerton had 1 piece construction.
2. Lugs had spring loaded inserts. Later in Big R era, the springs were replaced by clips to hold the insert in place.
3. Correct snare wire had 19 strands. Other will fit with no problem, especially from Puresound for player.
4. Throwoff had letter D stamped on it. It also had a "notch" when engaged to hold the snare rail in place. A Powertone throw will work also. Later 70's models did away with the D stamp.
5. Snare rail changed over time. Serial number required for "correct" piece.
Getting all the "correct" parts will cost more than buying a already completed drum. Recommend you go with parts that fit and make a players drum. I have seen some conversions with tube lugs that looked pretty cool. Thought about doing that myself with some black chrome rims and lugs against the chrome shell.
The shell has no snare bed, but many people have taken off the snare rail and put on regular snare wires. Drums still sounds great.