microcontrollers to start with
I would recommend the Atmel AVR 8-bit microcontrollers as a good starting point.  The micros themselves are a little bit pricey piece for piece for an 8-bit part, but for a hobbyist they're great, because the programmers are cheap, and the software tools are free (and excellent) These are the micros on which the Arduinos are based, and there are tons of examples for all variety of applications using the entire range of micros.  http://www.avrfreaks.net/ is an excellent resource if you're just starting out, and the people in the forum are extremely helpful.