Georgia Redfish, it's highly dependent on the needs and physical attributes of the individual practitioner.
Police Defensive Tactics (unarmed combat and suspect restraint) goes heavily toward the grappling side: Jiu-Jitsu, Aikido,Judo, etc. This is partly because of heavy legal liability considerations, and partly because their techniques benefit from finishing in a control hold that flows into handcuffing.
On the physical attribute side, the striking arts (Karate, Tae Kwon Do, boxing, etc.) tend to favor the physically strong, while the grappling arts tend to favor the fast and the flexible.
If you're only going to study one form, the most logical approach is an art that combines grappling and control methods with striking techniques: Hapkido, Hwarang-do, Krav Maga, Jeet Kune Do, Escrima and Kali, Pankration, etc.
In hopes that this is helpful,