You will not find a micro with this many hardware PWM options, but you can configure any pin as a software based PWM. On a micro with a port A, portB, port C, and Port D, there are 8 pins per port. You would use the RX and TX for your communication. this would still leave you with 24 pins using outputs of 3 ports for your PWM control and 6 pins left over which can be used as specific inputs for other tasks. Or, you could skip the whole RS232 thing and add a keypad and display.
One such chip that will work is the ATMega16. You can get chips with even more outputs than this one.
If you want a chip with PWM channels, Atmel has one with 10 PWM channels. It is the AT90PWM3.
Here is a link where you can get a comparison of all:
http://www.atmel.com/dyn/products/param_table.asp?family_id=607&OrderBy=part_no&Direction=ASC
MP