I would say aim for between 370-380 (others will have different preferred FPS'es, some even opting to run 330-350 and .28's which makes the BB even slower). I really like that range of speed for outdoor play. No real need to go to 400 FPS, however that said I have my rifle shooting a consistent 395 FPS but before that I was shooting pretty consistently at 355-360 the only reason I upgraded the spring was because I was in the gearbox doing maintenance anyways and thought I might do the spring as well.
As for the spring, I'd say go for an M110. M100 IIRC should do between 330-350 (depending on the consistency of your seal and air compression). M110 will do ~350-380. At the end of the day you're not putting significant strain pulling an M110 so it's probably good enough.
As far as battery goes, 7.4V is what I'd recommend for most people unless they want the best trigger response and a higher ROF. As far as battery care goes, get a good balance charger. I highly recommend the Imax B6 charger and the highest Mah battery you can comfortably fit. Also don't overdischarge your lipo or you may damage it or set it on fire (I'm serious), when you hear the ROF starting to slow down then disconnect your battery and switch to a fresh one (also you can get a lipo alarm that attaches to the JST-XH connector and will beep when voltage is starting to get too low).
Voltage = electric potential difference (how hard current is pushed through the wires)
Capacity/Amperes = amount of potential work available to do, aka "juice". Generally it's 1-1.3 BB's per mah on most airsoft guns so for a 1000 mah battery should last around 1000-1300 BB's/gearbox cycles.
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