Hi,
circuit is correct. You may use just one input and connect the other input to GND.
from where do the OR gate will get the continues Vcc
You have to supply VCC. Read datasheet on VCC supply range and supply current.
The capacitor discharges only for few moments.
It should be discharged at powerup. (to ensure this you may add a diode - anode to capacitor, cathode to VCC.)
Because of the feedback resistor it keeps it´s state.
On powerup it is low voltage, low input to gate, low output of gate, feedback keeps low.
On keypress it is high voltage, high input to gate, high output of gate, feedback keeps state.
Also using 74LS32 would be ok?
Yes. but "LS" has some drawbacks:
* needs more VCC current (An AHC1G32 needs only 1uA at 5.5V and 25°C, good for battery powered systems)
* needs more input current
* has a lot of pins. Mind to tie unused input pins to valid levels.
* needs 4.5 ... 5.0V (An AHC1G device may be supplied with 2.0V ... 5.5V)
Klaus