Use your start-up credits to get a Defender. Instead of taking missions, prowl the trade lanes. When they are disrupted, one of the fighters has to hold still to monitor the lane hoop. Blast the bejeezus out of it and tractor in its escape pod. Repeat this for the other fighters. If you want a fair, even-handed fight I suggest that you engage Liberty Rogues who fly bloodhounds instead of the nimble Xeno pilots with starfliers. Once you have a lot of escape pods go to the Texas system and sell them to Liberty Police, Inc. at Huntsville or Sugarland for a generous reward of credits. There are also prisons that accept escape pods deep in the Manchester, Shikoku, Hamburg, Alaska, Vega, Neophobos, and Sovetskaya systems. Use new-found credits to get a stronger fighter with more powerful armaments. Prey on easy-to-hit fighters in the Houses (e.g. Liberty Rogue wolfhounds in Hudson if you have a Dragon, Valkyrie, Anubis, or VHF) or begin to take NPC missions, continuing to tractor in and sell the escape pods. Do this at least until you have a couple million credits.
If you are willing to take a gutsy risk earlier on in the game, you can also get some easy credits by visiting the Sea of Shadows system. It can be accessed via a jump hole near that from Colorado to Galileo. There is a Bretonian base called the Ice Palace there, are a pair of wrecked Rheinland warships that will drop Codename weapons, if shot at, that you can sell. There will also be cardamine. As a cop, I must stress the importance of leaving that loot alone. Do not even think about looting it. Seriously. I am watching you. Always. Even when I am not logged in. Go about playing the game as if my Salin is lurking behind your six, stealthily cloaked, and within scanning range at all times. Because it is.
Hem... anyways...
In the systems surrounding X-3043 there are a broad selection of very heavy fighters to choose from. There are routes leading to X-3043 from every House - in addition to another route that is concealed deep in Outcast territory. A generous selection of vanilla Freelancer weaponry is for sale in the adjacent "Arena" system, and there are ship wrecks in most systems in the area surrounding X-3043. These drop Mk II codename guns, which will make it a lot easier to defeat NPCs in vanilla FL areas. There are also places to purchase class ten shields, which will make your vessel nearly invincible against NPC pilots who are human but not lieutenants or fighter aces. With time and/or millions of credits, it is possible to obtain equipment upgrades and better weapons that are scattered throughout Sirius, Altair, and the Inner Core. Explore, customize, and play the game on your own terms. Trading, smuggling, piracy, mercenary work, and mining are viable alternatives to capturing criminals - especially if you get a ship well-suited for getting the job done.
If memory serves me correctly, there are also four wrecks I am aware of whose commodity loot is worth a cumulative 39.6 million credits if sold at any dock in the game. I will not disclose the locations of these wrecks to you but will warn that all of them are stranded in systems with an alien presence. As a general rule, aliens should not be confronted unless you are in possession of a VHF. Even then, it is safer to go with a good wingman and carefully manage your reputation.
Fundamentally, your problem is not a lack of skill so much as your lack of a potent spaceframe that bristles with hefty weapons. Hopefully this is useful.