If you want just money, you have to pick your missions carefully. While several missions might have the same difficulty rating and pay about the same, it's a lot easier and more economical to specialize in "go to point X and kill the group of generic ships" than it is to assassinate or capture specific guys. What you want are missions you can handle with guns alone, so you don't blow part of your payment on ammo and shield batteries afterwards.
While you're still in Liberty space, the best place to for this type of mission is Norfolk (or is it Newport?) Shipyard in the New York system. This place offers a lot of difficulty 2-3 missions that pay $3-4k and often have AI wingmen with you from the beginning. These are easiest money in Liberty. You get paid a bit more in Texas and Colorado, but you have more expenses, it takes longer, and you're more likely to get jumped on the way home or while docking/launching afterwards. The other places in New York offer only level 1-2 missions that pay only $2-2.5k.
However, you'll also want some better gear than you can buy in stores, like Rogue Drails, Xeno Scorpions, and Junker Barragers. While you occasionally stumble across these on the "kill the generic ships" missions, the best way to find a lot of them is to take missions where you have to kill/capture a specific guy. This target is kinda like a mini-boss who usually drops a few good weapons. Even if you don't need them, you can sell a pair of Drails for $1100 so that makes the whole mission more profitable. But New York only has Junkers and Rogues as targets for these missions. If you want Xeno toys, go to Colorado or Texas.
So my advice is to go to Norfolk Shipyard and get rich on their missions, buying the best ship and stock/Rogue/Junker gear you can get. Then go to Colorado and assassinate a few Xenos for even better gear, although maybe no real net money. Then back to Norfolk for a big pile of money before going to see Juni for your level 5 mission
. Trust me, you'll need a PILE of money for that one
-Bullethead
In wine there is wisdom, in beer there is strength, in water there is bacteria