If you're worried that playing 2 might spoil something from 1, don't. There's no storyline to speak of in either game (although that might change with 3), and no real 'surprises'. In addition, the games actually play quite a bit differently from each other.
The first game bases its colony economy on a list of bars. Each bar represents the amount of money that you're spending on that segment of the colony, and can be adjusted to suit your needs. So you've got money that's being spent to increase industrial capability, build defensive missile platforms, build starships, research new technologies, take care of (or clean up) the environment, and maintain (or increase the population). In addition to providing new ship systems, tech advances might also increase planetary conditions by making it cheaper to maintain the environment, reduce the amount of population required to operate a factory, etc...
Tech advances were represented by six different categories of technology, which were all worked on simultaneously (although you could emphasize some technologies at the expense of others). Eventually, given enough time and resources, you could research every single technology in the game.
Ship movement range was determined by the maximum range that your fuel technology provided. The initial range was 3, which meant that your ships could move anywhere within three parsecs (i.e. spaces) of any of your planets. No need to return to base to refuel. You just couldn't move past this range.
You were allowed to have a maximum of six ship designs. Once you had more than this, you had to scrap an older one. Fleets often consisted of hundreds of fighters backed up by dozens of larger ships.
Hidden somewhere on the map was the planet Orion, which was a huge amazingly fertile planet with ancient technological artifacts, and guarded by a very nasty battleship called the "Guardian of Orion".
The Galactic Council met once a certain portion of the map had been colonized. The two largest races were nominated to rule the galaxy. Each race had one vote per system, and if one of the nominees got two-thirds of the vote, he was declared supreme ruler. If you won the vote, you won the game. If a computer player won the vote, you could contest it, at which point, every race would declare war on you. The other way to win the game was to conquer the galaxy (which involved abstaining in the vote once you controlled over two-thirds of the galaxy).
MOO2 had very different mechanics.
The races in the game each had their own advantages and disadvantages, but you could also create a custom race.
Planetary systems resembled cities from Civilization. Citizens could be moved between three areas (industry, farming, research). The bars from the original game were completely gone. Buildings were constructed (just as in Civ), and provided different enhancements for the colony (along with requiring cash to maintain). Which buildings you could construct was determined by the technologies you researched. While different research areas still existed, Technologies were clustered in groups of three (four?), and you could only work on one technology within each group (unless you had a special racial advantage). The other technologies within that group could only be obtained by trading with another race. You could also only focus your efforts on a single technology, as opposed to spending resources on a number of different technologies.
While the six ship design limit was removed, it was replaced with something very different. You could only have five buildable designs at one time (while you couldn't build other ships, you didn't have to scrap them, though), and you could only maintain a very limited number of ships. A single MOO1 fleet was often bigger than the entire collection of ships of all races in a single MOO2 game.
The same methods of winning the game were still present, but an additional method was provided as well. Mid-way through the game, an extra dimensional high tech race known as the Antarrans would start launching random raids against various planets. One of the tech advances would allow you to build a portal to the source of the raids, and you could launch a counter raid. If you won the battle, you won the game.