best for a core system is subjective based on your personal needs. uCs (microcontrollers) are usually best used when you need to have a more compact or energy efficient system. You usually get some built in flash (120k usually), a little bit of ram (12k), and some other various functions. This comes at a cost of speed usually, as the easiest to work with are somewhat slow (the Atmega 328 for example), especially accessing external SPI RAM or ROM. The more expensive ones can be hard to hand solder, but are quicker than through-hole offerings.
If you want to invest in something like this, try the mBed development board, it's based on an ARM Cortex-m0 platform, and should have sufficient strength for what you want to do. Once you get your code rolling, you can move your code off the mBed, and onto the target chip itself.
MPUs are best when you need more speed or a dedicated piece of equipment, usually they demand more power. they REQUIRE extra equipment to get them rolling. stuff like eeprom, ram, resonators/crystals, etc, all need to be added, the trade off is, access to these external devices are quicker. the more powerful ones are hard to hand solder, but if you have the capability to do it, they can be exactly what you need them to be. I haven't toyed with them enough, but I have a MOS 6502 derivative coming (the WDC W65C02S6TPG) that I'll be playing with in the future.
NSF and GBS playback would be best in software. If I recall correctly, they use a different APU. GBS really isn't complex enough to program a dedicated ASIC or FPGA). Both formats are relatively lightweight, as they were designed to use max 10-15% of the CPU load, so you don't need serious power. but take into effect that you're going to have to have an SD card or some method of storing audio data. so you'll have the overhead from that, the audio code itself, and whatever else you want to tack on.
for sound, look up the PCM2702, it can be used as a USB soundcard, but it should be sufficient for what you're using. Just be careful with plugging it into your ears to test, make sure the output isn't too loud, or you'll blow your ears.
The best place to ask about this is sparkfun.com, adafruit, or the make magazine forums. This topic is a bit out of spec for this place.