@SirW and any other casual player who's having a problem with the upgraded AI, you certainly have my sympathy.
I had a great and very intense weekend fighting in a Hi-RES at the bounty hunting CG in an Imp Courier, and while I had a great time I got shredded a few times. I did wonder how beginners and casual players could be expected to cope with the AI upgrades (and the improved modules the NPCs were sporting).
I ran a few of the new missions as well and the NPCs that bother you during the missions are tougher than those in the RES (maybe this is just because there's no authority ships around). So for casual players who like to run a few missions while travelling from system to system, it must be especially tough.
I'm going to give the same advice as many others on here, switch to a sidewinder or eagle for a while and head to a RES (preferably a Low-RES) to get used to the new AI. I bought a second account a couple of months ago to join in with community goals while I was out exploring with my main CMDR and I found it was really, really fun to be back in a sidewinder, it's a great little ship.
Against the old AI it was easy to make enough credits at a RES with a starter sidie to upgrade to a C rated Viper after a single visit. I'm not sure how well that would go with the upgraded AI, but in your position it should at least be easy to finance upgrading the sidewinder purely from RES profits. I'd just stick to that until you're comfortable taking on the NPCs.
With a starter sidewinder you just need to be patient, keep 3 or 4 pips in shields and don't shoot at anything until the security ships have almost finished them off (wait until the bad guy's shields are down and hull is below 50%). Then after making sure that they're definitely marked as wanted on your target display shoot them a couple of times and you'll get paid the bounty when the security ships kill them. The security forces have also benefitted from the exact same AI enhancements as the pirates, so the swarms of authority ships buzz around RES sites butchering pirates these days; you just need to wait a few minutes for the RES to fill up.
Lots of people have been recommending A-grade thrusters, etc. Personally if money is scarce, then I'd recommend fitting C-grade modules in a sidie / eagle / viper-III (if you can afford one). C-grade costs a fraction of the price of A-grade modules, but they're almost as good. That second CMDR that I got had a C-grade Viper-III and a C-grade Type-6 in no time at all.
If you enjoy PvE and don't ever wish to experience any threat of PvP attacks then as others have said, you really should consider the Mobius group, at the very least you’d be able to meet up with friendly CMDRs who'd help you out of your current financial problems.
To be honest though, the PvP problems in open really aren't as bad as they're made out to be, some of the current NPC ships are more aggressive than an human player that you're likely to meet. I've played mostly in open since the pre-launch days and I've yet to lose a single ship to a PvP attack (I've also not killed anyone). I've had half a dozen PvP encounters in that time, all of which were either in Leesti (which is deserted in open these days) or at community goals.
In contrast to that, I've lost 4 or 5 ships to NPCs since the AI update! Lol
So even in open mode, the game is pretty safe apart from obvious places like the starter systems and CGs. I normally stay in open, except for BH / combat CGs where I switch to solo in order to have the instance to myself. After a weekend of really intense solo-PVE in the Hi-RES, I had a quiet hour in Mobius at the trade CG, but I find that the instancing doesn't work as well as in open. I only met two other players at the CG in Mobius, there are always loads to players to meet at CGs in open (and often in Mobius, like I say the instancing just seems worse than open).