Also understand all the functions of the key.
Even in very old vehicles, the key locks the steering shaft and also powers up the Engine Run and Aux lines. So unless you cut up the steering column and disable the lock, driving will still require you to put a key in the column. If you leave a key in there, somebody's going to see it and break your window so they can steal your car.
And as I mentioned just pulling the ignition relay coil will only turn the starter. You also need to power up the Engine Run line which enables the fuel pump and computer, this will take a heavy relay. In fact in many vehicles this should be done a second before turning the engine over in order to let the fuel pump build pressure.
Then as noted you need a way to determine when the engine has caught. This is actually a pretty touchy procedure which is difficult to determine with a simple method, and there's probably no wire to tell you. The engine will be turning from the starter so a tachometer tells you nothing interesting. A fixed period may hold it too long or may not start the vehicle.
The keypad and driving tasks really need to be done with a microcontroller.
Carbed vehicles usually require you to pump the accelerator to set the choke, which isn't going to be possible. Vehicles with electronic "smart" keys are going to be impractical to bypass.