Hi Michelle,
My DH and I live in a 2 br unit with our DD. Our place is pretty big and it will even do for us to have our next bub for a little while.
The things that I think would be good for you to look for would be a place with not too many stairs- we live on the 3rd floor and going up and down 3 flights of stairs with a baby and shopping is such a PITA every day. Most units have balconies, so I think just be sensible like you said probably not one with railings but with brick or fully enclosed would be ok. You're not gonna leave bubs on the balcony alone anyway are you?!! Another good thing would be an internal laundry, it would be hard dragging washing around with a baby too. Lots of storage space, builtins or a storage cage. A bath or laundry tub big enough for a baby bath, much easier than an actual baby bath.
Can't think of anything else at the mo....