I would recommend strongly against the lightweight, small-frame .38 Special. They are concealable and convenient carry guns, but feature stiff recoil and a short sight radius. They feature a simple manual of arms, and are easy to learn how to operate but difficult to learn to shoot well. They are not comfortable guns to shoot and almost inevitably find their way into a pile of guns labeled 'shoot little, carry much.' Which is an OK pile of guns to have, but if you only have one handgun, I would say that is not the droid you are looking for.
In your category of polymer semiautaos, most of the common brands are more or less equal. If you're interested in maximum carryability, the S&W M&P Shield is an excellent choice, as are the Springfield Armory XDs, Kahr P9, Walther PPS, and Glock 43. If you want something with a little more capacity that is a little easier to shoot, step up to the M&P Compact, XD subcompact, Kahr K9, or Glock 26 or 19.
I think the M&P Shield is a great compromise between shootability, concealability, and cost, but you can also get the Bersa BP9CC sometimes cheaper, and that is also a fantastic value.
If you're interested in revolvers, I would recommend a six-shot, steel-frame .38 like a S&W K-frame revolver or Ruger GP100. It's likely you'll find these a bit heavy for carry, although it can be done with the right combination of holster, belt, clothing, and willingness.