Schlage, Kwickset, Titan are good lockset brands. If you go to a big box store, they can even re-key it for you if you get a compatible set to your key style. It's important to get a lock or latch for exterior use, not an interior one (bedroom or bathroom privacy lock).
It's not uncommon to have a locking deadbolt, and the handle not lock (this would not be a set), if you live in a place where casual crime isn't an issue. Otherwise you can get a lockset that has a deadbolt and latch that are coordinated.
I prefer lever styles for ease of use.