Prioritise actual missions for more Reputation
You'll buy cars, weapons and outfits in GTA Online much as in GTA 5 single player, but there's a difference: snazzier and/or more powerful items are locked off till you've reached a certain Reputation rank. It's fairly easy to increase your Reputation, but you might want to focus on the competitive multiplayer and Horde-style survival missions, as these award fairly decent Reputation and cash payouts even when you're on the losing side. I hear parachute missions (awarded by impressing a chap named Dom) are also good for some hefty payouts, though I haven't had the chance to try these out yet, and you can play these on your own if you click through before the game makes a match.
Pick fights with the cops - then flee
Riling up the fuzz is, of course, a time-honoured GTA pursuit, but there's a little more method to the madness in GTA Online. You'll be awarded Reputation points when you evade the police, so consider causing a bit of carnage on your way from one mission to the next - the enforcers of Los Santos are so feeble, that you should be able to slip the noose without diverging much from your route.
Exploit missions to get ammo on the fly
You can buy ammo from the lobby screen while waiting to begin a mission. Helpfully, you'll keep that ammo if you quit before the match begins. This can be useful when you're fighting somebody in free roam, and find yourself short of rounds - just fire up a quick round of Last Man Standing via the Jobs app on your phone, buy the ammo and drop out to resume the battle.
Join a Crew
When you join a Crew, you'll get Reputation points for assisting fellow members in-game - whether you're helping them in the world itself, or teaming up with them on a mission. A friend in need is a friend indeed. Plus, Crewmates are generally less likely to pull a grenade launcher on you for absolutely no reason.
Good Sports get prizes
Tempting as it may be to run or gun down every player you see, trotting innocently about your world, this isn't advisable. For one thing, renegades will eventually be branded "Bad Sports", which makes it less likely that you'll be matched with honourable, decent folk in missions. For another, players who help each other out, or at least don't kill each other on sight, will become "Good Sports" and receive automatic cash payouts at intervals.
Remember to bank your cash
People can nick your cash when you die, so make regular trips to an ATM in order to offload the green. If you're short of money, you can also, of course, camp an ATM in order to pick off other players just before they make a deposit. [Update - For maximum safety, deposit money by accessing the bank's webpage on your phone.]
Stores are safezones
Getting the worst of it in a stand-up fight? Run into a shop, quick - PvP is disabled while you're inside. Believe it or not, I've had the opportunity to test out this tactic in real life.