[Steve DeRosa]

My experience:

• Experiment - strings are one of the cheapest hacks for customizing both tone and playing feel
• Use the heaviest strings you can handle compatible with your preferred style, especially if you've got a "classic" electric (Tele/Strat, LP/SG, any hollow/semi-hollow) - more vibrating mass + higher tension = "bigger" tone, and you won't need to sink a couple hundred bucks into upgraded pickups down the line (My '86 MIJ Squier Strat has the original PU's and flatwound 12's, and it can - and has - go toe-to-toe with some of the best USA stuff)
• Consider a wound G - I've found better tuning stability and more consistent tone/string-to-string balance (an unwound G can generate strange harmonics with certain guitar/pickup and hardware combinations), and the transition is easier if you play both acoustic and electric in the same set, particularly if you go with a similar gauge (11's/12's) on your electric
• If you're a speed player - in whatever style - flatwound strings will let you set your action lower than comparable-gauge roundwound/half-round, without rattle or fret buzz (something the '50s Bop-era jazzers and rockabilly cats understood), and there's something very seductive about that sweet, mellow tone (try a set on your LP, and you'll see why it was originally conceived as a jazz guitar with increased sustain)

YMMV...