A garmin 200? I thought the op wanted cheap? That unit is not cheap at around $130!
You get more features and greater reliability at a lower cost with wired units then wireless, but some people like the clean wire free look, so you have to decide that part.
Cateye still makes a rugged wired computer called the Enduro that comes with heavy duty wiring if that's what you need, but I don't see where in the instructions that it will hook up to more then one bike but it is cheap at $24, you could get 3 of those for almost half the cost of the Garmin!
I personally like Sigma computers. The BC1609 has everything you want with automatic recognition of 2nd bike but you do have to purchase the second mounting kit that comes with sensor cable and handlebar mount. This unit also has wired cadence sensor, if you desire another cadence sensor for bike 2 then you would have to buy that as well. But the cool thing is, this computer is only $30 plus $8 for the cadence wire and sensor if you want it. Some places sell them as a package but you will have to look around for that; the extra speed sensor and mount for bike 2 is only $12.
Everyone has their favorite computers so this is going to be all over the board. I suggest you study on the internet the computers being suggested here to find the one you think you'll like best.