Seeking advice. Any electronics wizards in the house?

What sort of development board or hardware should I look into if my goal is to drive a QVGA resolution display at 60Hz?

For background, I've wanted to dabble in the world of micros for a while. The only other things I've done with electronics are power circuits and a bit of logic (e.g. gates, shift registers). Before the Arduino craze I picked myself up a PIC development board with the best intentions, but I've found it's hard for me to dedicate time to learning unless I have an end goal in mind.

After reading an article about interpreting/decoding the original Game Boy's LCD data I think I have something in mind now. I'd like to do something like that, except have hardware that reads in the LCD data and outputs it to another display. It seems like something that would be fun to do, and I could experiment with simple scaling methods for the output like doubling the horizonal/vertical resolution and having the discarded lines be adjustable. The concepts (scaling, color-space conversion) are familiar to me in pure software, but the hardware and tangibility will be a learning curve.

Having no significant experience with this kind of hardware though, I'm not sure how powerful of hardware I may need or if micros are even the best choice. From what I've been able to gather, an Arduino would struggle to drive a display of that resolution, let alone do processing in addition. Then I've found more promising things like the STM32 series of micros, which are more powerful and have development boards that ship with QVGA displays, but I have no idea what would be best.