well, pretty good advice for the used bike purchase. pretty much anything solid and reliable with no-too-skinny tires and low gears... i use a mountain bike fitted with a rear rack and fenders and lights. an old mountain bike with or without front suspension can be a great utility bike choice (wide tires, low gears, good brakes)

as to your current bike. there are 3 options:
1) use a backpack. here you can't carry as much stuff, but any bike will do
2) add a rack - although most racing frames no longer have eyelets. my old MTB does not have eyelets and i "built" connectors using hose-clamps from the hardware store. has lasted for some 5 years now. then for your recreational riding the rack will either be a pain (more weight) or you will have to remove it (i am lazy about such stuff)
3) seat-post rack if you have no eyelets (also for full suspension but not appliciable here). these allow you to strap something on but the one i have doesn't let you really carry panniers (there no place to hook onto below to keep out of rear wheel, plus no lateral stabilization)
4) use a trailer - they aren't cheap, but trailers are great as you can carry a LOT and you don't have to modify your bike - i.e. unhook and pretty much ready to ride fast/race... if you do SERIOUS shopping and really want to be car-free, a trailer is the way to go as you can carry heavy as well as long/awkward loads. (i have a BOB trailer which is also good for touring and off-road riding, but for utility there are other cheaper/beefier options)

between my 4 bikes i actually do all of the above with trailer hitches on 3 of them, racks on 2 (plus a seat-post rack that i rarely use for the full-suspension) and then nothing on my skinny-tired road-race bike.