Originally Posted by cooker

There are lots of options.

The most popular choice is a "normal" rear rack that attaches both to the frame just above the rear brakes, and via support struts screwed into brazed on eyelets on the rear drops, which most bikes have. Often there are two sets of eyelets - one for a rack and one for fenders. You can then get a pannier or a pair to attach to one or both sides of the rack. You have to make sure the pannier mounts high enough or far enough back to avoid heel contact. Often the rack or pannier have some adjustability. Or you can simply bungee your luggage to the top of the rack or get a trunk bag that sits on top of the rack. Or you can attach a crate and just drop your luggage in that. I don't like crates on my rear rack, because they crowd my butt and also it's hard to swing my leg high enough to get over a crate. (I'm kind of old.)

If the bike doesn't have the rear eyelets you can attach the struts to the frame with P clips, or get a rack that only attaches to the seat post. I don't like seatpost racks - they hold the luggage too high and may even sway a bit.

Some touring type bikes also have eyelets on the front fork for additional panniers but usually they are used for additional storage after the rear ones are full - for example for long distance touring. Occasionally you will see an actual front rack shaped something like a rear rack, but they are rare.

Then there are bikes with front baskets, usually made of wire or metal slats or you can get wicker ones. Those are usually on upright, comfortable, Mary Poppins types of bikes that are a bit slow and leisurely for casual city use and I think they may ride a bit ponderously but I haven't ridden one for year so others can comment.