You're on the right track dude, although with minors I wait and trade techs with them before I kill them. I get all the techs, and they don't get to sell mine on to others. I also get a juicy planet at the end.

Here are some other general tips:
I don't know if you already do this or not, but on the first turn go straight to the Domestic Screen and set your spending capacity to 100%.
Don't be afraid to adjust the economy sliders. In times of peace, you can often get away with a very high Research %, so when you do need ships they're top of the range.
Don't research too many ship and weapon techs at the expense of production techs. There's no point having the best ships if it takes 20 turns to build them at your best planets!
Don't research improvement techs too quickly, or your new worlds will take forever to develop (unless you're a rich bitch).
Unless your planning on killing everybody quickly, it might be a good idea to go for Trade early to make money. There isn't a lot of point setting up trade routes with someone you're going to kill.
Don't build too many improvements at the beginning, or you will spend too much on production and go bankrupt.
If you want big ships, don't neglect logistics.