The outposts come in 3 sets of three totaling at 10 outposts. Each following set uses a rarer core to power it. However if you abandon an outpost you do not lose those power cores.
Now for the first 3 outposts after your comand center you will need 2, 4 and 6 base power cores which are the easiest to find. For the next three bases which will number 5-7 you will need base fusion cores and take 5,10 and 15. The next three bases will use base plasma cores and my guess is it will take more cores then the previous set making it very hard to get the full 10 bases together without paying real money.