Domain star-gate: Extreme convenience value. Requires completing plot to get that value, but once you get there, it's worth it.
No Atmosphere: Required to use the colony items for refining & fuel production. Also a good place for Heavy Industry - it's not habitable, so you won't get pollution from installing a nanoforge, and having refining on the same planet as heavy industry means that you won't get trade fleet disruptions shutting down your heavy industry. (Heavy Industry isn't going to turn much profit without a pristine nanoforge, but it is the thing that lets you make use of your own blueprints.)
Adding ore & rare ore means you can install a mining colony item & get a full sequence of mining feeding into refining feeding into heavy industry, making all three immune to trade disruptions. It's not necessary, but it's nice to have.
At max size, this planet will have refining, heavy industry, fuel production, and either mining or commerce or maybe a military base.
Gas giant: Allows installation of the other mining colony item - the one that boosts volatiles production. This will almost certainly be a high hazard world, so you build mining (which is cheap) and maybe some minimal defenses to get it over 5 stability, and then you mostly leave it alone.
Habitable world w/ food & organics: Fills in the rest of the production options: food, organics, and organics feeds into light industry. This is important less for the direct monetary production (though a good planet can turn a decent profit off these things), and more because your colonies get a maintenance cost discount for each of their needs that can be filled from in-faction sources.
Being near the core improves accessibility rating, and makes it easier to get to and from the place before you've finished the relevant plotline for the gates. Useful, but not vital.
Domain era comm relay is an extra +1 stability for every planet in the system. Definitely nice to have, but also not vital. If you don't have a domain-era comm relay already in-system, you'll need to build a regular comm relay - you can interact with an empty stable point to do this, at a cost of... I think it's 100 metals, 10 transplutonics, and... 20-ish Heavy Machinery? (Or, technically, you can build a patrol HQ on a colony and then let your patrols fill in any empty stable points, but you probably want the comm relay sooner than that would complete.)
If your system has no stable points, interact with the star - that'll give you the requirements for adding one (and then you can build a comm relay in it). If your system has one stable point, and it's got a domain-grade non-comm-relay, you can still interact with the star (but it'll be more expensive). If your system has two stable points and they're both occupied with things that aren't comm relays, you'll have to dismantle one to make room.