Nirth: I did some mining and upgraded what I can but I'm still only level 4 so it made no difference. I now have 1300 rez at least, I'll see how it goes and read the thread you posted.
You need data to gain levels. There are basically three ways to gain data. Whenever you kill a ship, a few data nodes are left behind. Secondly, occasionally you'll come across a bunch of crates and spheres floating in space. Some of them contain data nodes, some contain crew members (goons), some contain rez and some are empty. Finally, some of the tasks you can perform for the UTA and civilians in the various star systems give you data as a reward for completion.
When you gain a level (i.e. when you have collected enough data), you get a number of upgrade points. Use these in the research interface to upgrade your technology levels. Try not to spend points on technologies you don't have access to anyway, meaning if you haven't bought any drone designs, don't bother to upgrade drones in the tech tree.
Technology upgrades don't automatically give you access to better equipment. You will need to purchase designs from UTA and civilian space stations in order to get the equipment. You can buy all the designs you want (if you have enough rez), but in order to use them on your ships, you will need to have a high enough tech level in the appropriate technology. Some designs come in many parts, and you will have to buy them all (from different space stations) in order to use them.
New ship designs can only be acquired by destroying ships of the particular type you are after. Like the equipment designs, you will need a number of these for each ship before you can reverse engineer the hull design completely, but once you get enough, it becomes available automatically.