another advantage of a rear rack (besides much greater stability---none of that weight on your handlebars), is that in addition to panniers (the saddle bags), you'll also be able to put another bag or strap things to the top of the rack---good for when you don't want to shove your diaper bag/other tote into the saddle bag; just bungee it and away you go (but make sure nothing's hanging down to catch in your wheel).
check to make sure you can install a rear rack: you'll generally need securing points pre-drilled into your frame on the seat stays (or the seat stay bridge) and the drop outs (the rack will come with screws to screw into these points).
Alternately, if you tell us the bike you've got, we can tell you if it'll work (chances are it will; most bikes have these except for extra-light racing bikes). Alternately, if there are no pre-drilled points, there are plenty of adapters that can still make it work just fine.