A lot of talk about FPGA and CPLD which is great, but doesn't necessarily address the original question of what to use.
I would say that if you are starting with MCU experience, then PSoC is going to be the easiest and most productive for you. I think the Cypress PSoC chips are phenomenal, and the dev kit that miguelvp posted, this one:
http://www.cypress.com/?rid=108038has to be one of the most screaming deals in dev kit history. It's a top-of-the-line 80Mhz ARM Cortex M3 processor with lots of programmable digital and analog logic.
Whereas a standard MCU will have 3 times, 2 PWM's, 5 interrupts, an ADC or whatever, the PSoC chip instead has a given number of 'blank pages' (programmable blocks). You can put whatever you want on those pages... if you need 20 PWM's, you just keep adding PWM blocks - you can add as many as the chip has free blocks. You could add 10 SPI channels, 8 timers, 20 interrupts, an LCD controller or whatever else you want. There are also pre-built functions that you drag-and-drop into your project that do things most other chips can't do in hardware. Things like quadrature decoding, fan speed control, LINbus, shift registers, switch debouncers, SDM modulators, or whatever. There are also 3rd party components like those to drive WS2812 LED's or interface with unique LCD's. You can also write your own stuff in Verilog/VHDL although it's not made to be easy as it would be with a dedicated FPGA tool.
Anyway, that board posted above is $10 and includes a programmer, just plug it in your USB port and that's all you need.