All breeds have homing instinct, but only homers have reliable homing ability. What I mean by that, is they all know to go home - to come inside to perch/roost, eat, drink, live. They won't fly away like parrots or doves will if they escape the house/cage. HOWEVER, the majority of the breeds cannot go out of sight of the loft without getting lost. For example, say you live in the woods, and your bird is chased by a hawk until it cannot see the loft from all the trees. If it gets up and tries to find home, it will either get lucky and see the loft and its flock, or it will go the wrong way and get completely lost. Flying breeds have a better chance of getting up high enough and seeing familiar places.
If you want pigeons who can fly here and there, and wander around like free ranging chickens, then you're good with just about anything (try to stay away from the show birds, as they are usually much slower and easier to be picked up by hawks/other predators).
If you want pigeons that when you let them out, they will fly as a flock, above the trees, making laps around the property, and want to get entertainment out of seeing them fly, you'll want a flying breed like homers, rollers, or highfliers.
If you want pigeons who will also be able to fly home from distances up to 600 miles (or more, if they are good and you are good at preparing them), then your only choice is homers/racers (same breed, slightly different purposes).
Messenger pigeons were homing pigeons. They come home, as in one home. If they were too old when you got them, and you let them out, they'll fly back to where they came from. Yes, bases did move around a lot during the war, and lofts had to be relocated a lot. But they were very good at what they did, and young birds were being bred and provided by fanciers constantly. There were a LOT of pigeons that served in the World Wars.
