An 8.4V Nihm or Ni-cad is really the base option for most guns. A 9.6V Nihm would work fine without any changes to your current gun and would "probably" charge fine with your current charger for your 8.4V. It would also give you an increase in ROF and probably speed up the trigger response as well.
Changing to a 7.4V Lipo will give you about the same increase as using a 9.6V Nihm, but will involve buying a different Lipo specific charger (Lipos charge through the small white balance lead, not through the connection to the motor lead), as well as the Lipo itself. Unless you go for a higher mAh Lipo (e.g. the 2200 mentioned) then you might need to buy a second one to change at lunch if you are trigger happy. Alternatively, buy the Lipo and keep the Nihm as a spare, although to be perfectly honest a change to a 9.6V Nihm even as a spare would still be worthwhile, as they're not that expensive from Componentshop.
Don't even look at an 11.1V Lipo unless your gun has a really strong, upgraded gearbox, as the extra power of a 11.1V Lipo will overstress most any bog standard gearbox and result in a fairly quick breakdown.
