Hmmm, well...yes...read on for mild spoilers...
Delta Centauri (IIa, IV, V, IV) and Beta Centauri (Ic, IIIc) are close to home and are very rich with minerals.
Delta Tauri is also close and has a ridiculous amount of minerals. Focus on I, II, III, IV, and VII.
You'll meet a race that is friendly and willing to trade you upgrades (the lander ones are the most useful right now) for either biological units or the locations of certain "special" worlds.
The location information is worth a LOT in trade value for them, so try to hunt these down.
The closest location of this race is at Alpha Centauri. They'll be roaming around and sometimes you have to go near each planet of Centauri to find them. Sometimes they are just out in the open on Centauri.
The closest "special world" is at Zeta Sextantis I.
Once you get all that you want from them (info and upgrades) you can rack up easy res units by doing the MTM trick...have them fill up a bunch of your fuel tanks and then go back to the StarBase. "Unfuel" the tanks for 20 res units per gallon.
I'd suggest doing that later though.
There's another race who likes to trade with you, but they are quite evil. There's an even better trick similar to the MTM refuel trick that will (a) give you a ridiculous amount of fuel and (b) result in a hilarious dialog where they realize you tricked them.
With them though, don't give them anything you truly need, only give them doubles of stuff you have. One of them is an extra communication's device and the other is a particular fragment that you'll find.
Regardless, have fun...and don't get discouraged...save often and that will allow you to experiment without worry. I like to save one game ("going to mine Centauri") and then save into another slot as I mine each planet. That way if you blow up you can restore from your last good mining attempt.