Ideally, the system should have
* A gate (very convenient once you have Janus Device)
* Habitable planet (for farmland and organics)
* Planet with no atmosphere (for fuel production with synchrotron, at least)
* More planets to get missing resources (e.g., gas giant or cryovolcanic for volatiles)
* Close to core worlds (at least close enough to avoid isolation penalty)
The lower the hazard, the better. Avoid planets with more than 200% hazard.
Ideally, you want all planets in one system for maximum defense against invading forces, but if that is not possible or optimal with the current game, then colonize two systems, one with three colonies and another with two.
The only colony items you really need are synchrotron and a nanoforge, ideally pristine. That is because Military Base and High Command have demand that is impossible to meet with Industrial Planning and colony improvements alone, and items, whether colony items or Alpha cores, are needed to meet them.
Those special areas are either sleeper ship or hypershunt. Sleeper ship enable building revival structure that boosts population growth. Hypershunt requires a tap to use and other items to get the required transplutonic ore to feed the tap, and your reward is +1 to maximum industry slots.
Pather cells will appear on size 4+ planets with 7 or more interest. Mining adds 1, Refinery adds 2, most colony items add 4, hypershunt tap adds 8, AI cores in various buildings vary by type, and Alpha core administrator adds 10.
Using any AI cores at all on a colony will eventually trigger inspections from Hegemony.