The first idea is not so easy to realize, as you need a lot of keys with printed caps, which are hard to find now. That was the way we built computers 35+ years ago!

The second one is much easier, but you need some MCU converter with quarz or ceramic resonator stabilized clock. PS2 outputs clocked serial signal and it is theoretically possible to use DATA only as asynchronous signal, but various keyboard use different clock rates. They are generally about 10-30 KHz, and they use low-cost and low-stability RC internal oscillators, surely not good enough for asyncronous RS232.
So you need DIY controller with 2 inputs (data and clock) and one serial data output. The advantage of this is that you can add macros, automatic messages and so on.
There's a good PS2 explanation at
http://www.computer-engineering.org/ps2protocol/By the way, first PC keyboards for XT costed about 700 DM in Germany. Also, I paid my first mouse 600 DM, it had only 74LS04 buffer inside, for optical encoder signals and connected directly to Olivetti keyboard, where it simulated keyboard arrows.