For lipo you'll need HV servos, it'll fry the stock ones. I recommend a "hump pack", which has 5 nimh cells, so it drives the stock servos about 25% faster than 4xAA nimh's. On the plus side, it's even cheaper, and pretty unlikely to catch fire.
As you intuit, the next step in servo power is indeed a 2S lipo system. You'll need servos that can take that, labelled "HV"; non-HV hobby servos will burn out on 8.4V. Most receivers can already take the increased voltage and most have the acceptable voltage range printed directly on them, so...