if the big city you're referring to has a bike share program, i would do that and have that be your "cheap bike"

pros and cons: you have it always but have to renew which adds $$$ to your "beater" so first year $150, second year $150, third year $150 and so on...
if you buy a bike but it gets stolen in a month then you add $$$ to your "beater" so first bike $150, stolen - buy a second bike for $150 to replace it - for year one.

but if it doesn't get stolen, it's a free ride that pays for itself for sure.

in a big city i would do the bike share b/c you can combine transit rides and bike rides and don't have to worry about bringing the bike with you if you decide on transit. that said, a bike share dock isn't everywhere here in NYC yet so... :/ hard to say.

i use a cyclo cross bike and i have pitlocks for the wheels, stem and seat (similar to pinhead) and i use a NY Kryptonite lock. but i know b/c it's NYC, it's very possible i'll never see my bike when i lock it up outside.