Think a little before you go all-guns blazing and you'll be able to earn cash and Rep in no time at all.
A lot of early straight character missions (star icons on the map) can be done with a single player but remember that any jobs done with a group earn 20% more RP. Do these to get a fair bit of easy money and RP, and remember to grab any money dropped by the goons you kill. It all adds up.
Generally in missions where you have to steal a package you'll have a shootout followed by the opportunity to grab the drugs and get in a car before returning the package. At the point where you enter a car another wave of enemies will try and chase you down. It's much easier to grab the coke, jump in a car and then get out again immediately and face the enemies instead of trying to out-drive them as they will shoot your tires or worse - you.
AI enemies in GTA Online are pretty predictable, so use a vehicle for cover and pop out to shoot them down systematically. This also gives you the added bonus of walking over their corpses and picking up any loose change. You can now drive to the destination and drop of the package with no hassle at all.
You can do early races on your own. It's boring but you always come first so it's money in the bank and you learn the layout of the race before going against real people. It's also handy for learning to fly the various planes, which can be pretty tricky. Look for flying races that force you to fly under a bridge as you earn extra RP.
Contest games (a suitcase icon on the map) are good for money and RP, and Survival (a cross icon, unlocked around level 15) are great for stocking up on bullets and new weapons, as well as RP. But they are tough and will test your gun skills.
Liquor store robberies
Robbing liquor and convenience stores dotted all over the map are fun. Firstly, make sure you've got a mask from the shop on Vespucci Beach as you can remove it after the robbery to lower your wanted level.
When you arrive at the store aim your weapon at the shop keeper. you can intimidate him faster by shouting into your microphone, shooting up the shop and keeping the gun pointed at him. If there's a second cash register on the counter, shoot that for extra cash.
Once he's handed over the bag of cash you can either shoot him and take whatever he drops or get the hell out of there. Shooting him raises you wanted level by another star. Getting away from the cops with three stars is easy enough if you're confident, and you'll earn extra RP for evading them.