The 1960s HeathKit Programming systems 

Nice! 10/10, would learn a lot of low-level stuff the good old hands-on way.

Market launch was in 1977. The ICs on mine are almost all dated 1981.

You should be really careful about connecting wires to those small holes on the PCB itself, those are likely vias (connecting top and bottom traces of the PCB) and you may end up short circuiting something resulting in damaged components! If you connect an output pin of the CPU to +5V and the CPU then tries to pull it low, the output stage on that pin could be permanently damaged! Also, yes you can certainty get those 74xx series IC-chips even today (I have used a bunch of them to create my own 8-bit CPU like Ben Eater did). Just remember that the 74xx series only run 0-5V and NOT +/- 12 V! - Those voltages are usually only used for operational amplifiers or similar analogue systems.

Looks more like late seventies/early eighties , certainly NOT sixties, all those IC's and microprocessors didn't exist back then, only transistors, diodes, resistors, capacitors, potentiometers and that kinda stuff

@jefftranter made a video about the 3200 at ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-eIInXZuFsRQ.html and another about the 3400 at ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-EjYpuwnf2wM.html