I've taken a recent shine to Split vessels as a player-piloted ship, their Heavy Dragon corvette is a seriously powerful customer. Otherwise, an Argon Raider-variant Nova is always a solid choice, if rather un-specialized.
Early on, I simply try to stay alive, maybe make a small trade transaction here or there if I'm on a low-balance start. Once I'm in at least a decently-fitted M4, I can think about carefully trying to capture other fighters, generally Pirates and smaller than me. An M3 will squash anything smaller than itself with near-contemptuous ease, but persistence and knowledge of your foe can overcome an M3 in time. Just be smart about engaging a turreted M3 if you're outclassed.
Once I'm sitting in my own M3, I shift away from primarily roaming and looking for trouble to setting up a trading business. Capturing ships and scavenging is still a great way to make money, and I often bootstrap my first TS with funds from a captured M3. Outfit a TS with Mk3 Trade Software and send him to a safe system to start autonomously trading (this will cost about 1.5mil Cr/freighter). I actually let X3 run in the background near-constantly when I'm actively working on a game, and my traders often make back their cost (or close to it) overnight on normal speed. This is also a simple and neat way to Universe-qualify your traders in a "hurry".
When I have about a dozen Universe Traders working for me, I'll try to get my own TL so I can deploy my own factory stations with minimal hassle. There's still a lot of hassle involved with stations, but having a TL simplifies one aspect of that. Argon Prime is a good place for a modest Power Plant; there's a lot of demand, and the local Crystal Factories should feed your own demands. Factories tend to make less money than traders, but they're a lot more consistent.
Eventually, I'll settle in a system and plop down my own HQ Station and potentially Shipyards (I played a lot under the XTC mod, and I don't quite remember exactly what can be done in vanilla TC). I try to hold out for my own large station before upgrading my personal ship to a capital ship; first one's usually an M7. Late game begins at this point, and I start to reverse-engineer any ship designs I happen to like, while amassing resources to build them from my own mines and foundries. In my last game, I finished off by launching an all-out assault on the Paranid Empire; my armada destroyed fully half of their inhabited systems before X3 said "no mas" and crashed. Naturally my latest save was hours ago.
I tend to pick up X3 pretty hard during the summer, if there are any more tips/tactics you'd like to know, just ask.