Minor civs are exceptionally easy to conquer, you just have to plan it out right.
They generally have only one system, so they are limited to 16 ships in orbit ... now if they haven't been in a fight with anyone before, a whole lot of those ships will be stuff they've built since the start of the game (star fighters, corvettes, maybe a few battleaxes). Even if the minor has battleship technology, if their orbit is full, they won't be able to build any big guns. A few frigates/battlecruisers (for the battleaxes), along with a nice stack of corvettes (for corvettes/starfighters) will usually wipe out a minor set up like described above.
An even easier method for minors, assuming you are reasonably close to them, is to make a research beeline for the impulse drive (gives you Transports) right off the start. If you do this quick enough, you can send over a transport while the minors have their pants down (they won't have military ships in orbit, just 2-3 colony ships "defending" the system). So all you need is a starfighter/corvette, or your survey ship upgraded with 1 attack to clear the orbit, and land your transport.