I have been away from stamps for a while now, so maybe someone else will have a different opinion. I got up to a Basic Stamp 2 device (BS2), which they still offer, but are currently out of stock. For about $10 more, there is a faster BS2 SX. You would need a computer with a serial port, or a usb serial port adapter, to program these Basic Stamps.

For a comparison on their capabilities, you can see this: http://www.parallax.com/tabid/436/Default.aspx . Just click on the different stamps you want to compare. The BS2 is capable of what you describe, and probably the Basic Stamp 1. But I would definitely get a BS2 or above, rather than the BS1. A lot of the code transfers pretty easily, if you want to switch to PBP later on.