I've heard incredible things about this two games series and was thinking of purchasing one of them. I have no foreknowledge about any of them; the most similar thing I've played is Sins of a Solar Empire and loved it.
I'm completely in your hands on this one!

Well aside from both being space-set classics, they are very, very different. Master of Orion 1 & 2 are 4X turn-based strategy games while Star Control 1 & 2 are more action/adventure with some strategy thrown in. I would say Master of Orion is closer to Sins despite being turn-based rather than real time. Personally I love of Master of Orion 2 and there are quite a few people on the boards here who prefer MoO1. They play slightly different from each other.

Each of these games are classics of computer gaming, are very influential on the development of modern 4X games, and in many ways are still every bit their equal despite the "datedness" of the graphics. They both feature turn-based strategic and tactical maps, allowing you to make high-level imperial decisions and also engage in tactical combat with ships you design. Each offer different takes on Imperial management and some may prefer one over the other. In MoO1, much of the direction is handled by funding and research sliders which stipulates how much is to be spent on each area of the economy and how much expertise to assign to each research field. In MoO2, one has discrete population units assigned to various lines of work and you build specific buildings to your colonies. In MoO2, you research one field of study at a time. There are of course many other differences, but these cover the basic differences in management between the two games. I copy-pasted this paragraph from my review of the games, hope it helps. :)

Oh and welcome to GOG and the community forums!

Thanks for the help, people! I've bought MoO 1+2 and downloaded SC2 (The Ur-Quan Masters) for free.

You were right; both are awesome but completely different. MoO is like a Civilization meets Sins of a Solar Empire, and SC2 has some management options but is basically action-centered (ME planet mining is really based on this).
The two of them very original in it's own way and the retro graphics add charisma to them. Quite unknown gems.

Glad you're enjoying them - some quick tips

For SC2:

There's a boring early period of harvesting (yes, ME2 copied the boredom aspect nicely, well done), use it to upgrade your flagship with better maneuverability, speed, and then some weapons - you can avoid most early conflicts without too much trouble.

You will get upgrades and discover extra means of earning RU that will make gathering much quicker.

Once you have some upgrades, start investigating any and all rumors and sightings of aliens - there is a 'critical path' to the story, but its extremely flexible, and you can investigate all manner of side stories along the way, and there are some events that are entirely in your hands as far as how they turn out, some with extreme consequences.

For MOO2:

If you're comfortable with Civ, you should have very little trouble jumping in here. Dig around online for a walkthrough or strategy guide to pick up on any areas that might seem obscure.

Ship construction and research can be a built overwhelming early (but in a good way!). Most new players start with Creative races, then graduate to others once they have a grasp on the research options.

For MOO1:
Again, its pretty darn crusty. Assuming you do dive in though, a few thoughts.

The main reasons its awesome are a randomized limited tech tree (you don't get every tech every game, forcing you to play around their absence or acquire them via trade, espionage, or ground conquest (raiding factories for salvaged tech, essentially).

The second is its colony management - a handful of sliders and you're done. It seems 'too simple', but you will be grateful for it later in the game when it takes so little time to manage, leaving you to focus on combat, diplomacy, and expansion, the fun parts :D (this is exactly reversed from MOO2, which bogs down the later in the game you get due to colony micro - I play on medium maps rather than bigger ones for that reason).

MOO has very little in-game help however, so a lot of mechanics are extremely unintuitive. Check out this fan-faq: http://www.gamefaqs.com/pc/564694-master-of-orion/faqs/1927

Again, the OSG is actually really good and an interesting read, but tracking down a 15 year old guide for a game you may or may not like is probably going a bit far :P

Thanks for the tips. For the moment I've completely ignored MoO1. Still getting familiar with MoO2; I've already beaten the tutorial and easy mode the pacific way, becoming Emperor of the Galaxy though elections.

SC2 really starts very slow, but has a lot of personality (the conversation with the weird alien in Pluto is hilarious). Right now I'm doing what you said; gathering materials for ship-upgrades not far away from Sol.

I haven't read it yet, but the manual of MoO1 that comes with the game in GOG is quite detailed I think (tracking down a 15 year old guide of an not very known game is indeed difficult).