Science & Industry

Sisters of EVE does have their own faction, but does not hold any high sec systems. The only reason to run missions for sisters of EVE is to use loyalty points to buy sisters probes and launchers, the best in game and they sell well.

You need faction standings.

For example lets go with Caldari as it is very popular due to Jita being in the Forge(Caldari Faction Space).

You can run missions for any Corporation belonging to the Caldari Faction. Lai Dai, Caldari Navy, Hasyoda, It does not matter. But the corp standings you get will not allow you to anchor a POS, you need faction standings.

How do you get faction standings?

-As you know you get a faction standings boost for each storyline mission you run for any corp of that faction. You need to run 16 missions of the same level for any corps of the same faction to get a single storyline mission.

-The tutorial agents you get missions from at when you first start the game are all storyline missions. There are three groups of tutorial agents for each faction. run them all. This will give you a great start. You do not have to be a member of that factions race to access these tutorial missions.

- There are also a series of missions known as the COSMOS missions. these start a level1, and got right up to level 4. each missions chain in the COSMOS missions is a storyline. You can get a huge faction boost running COSMOS missions. But be cautious, some require items that take a lot of time to farm, get the items before accepting the mission, or just buy them from contracts. Some COSMOS missions will take you into or through low sec, but this can make you huge isk. There is a level 4 COSMOS mission that includes the Michi mining implant as a reward. The implant is worth billions. But the mission is on a high sec island, you need to pass through a heavily camped low sec to get to it. COSMOS missions can only be done once per character. if you fail to complete a mission ned for the next mission in the chain you will never be able to retry the mission.

- Then there are data centers. Basically these take tags in exchange for standings. Farm or buy the tags first as they take a long time to farm.

- Then there are the epic arc missions. there is one for each major faction. You need fairly high standing to access them, but the isk and faction standings are well worth it. These can be done once every 3 months I believe. I generally run the Caldari Epic arc and get the hyasyoda Lab reward. I used to be worth over 1 Billion isk but know is only worth about 250 Mil.
You will also want to train social skills to at least 4. These skills either directly increase the amount of standings gain you get from each mission, or in the case of Connections if increases you effective standings. Effective stands do nothing to directly help you faction standings, but can allow you access to agents sooner allowing for high level missions with higher standings rewards to be run.

Standing take a long time to grind. But are well worth your time as there are many benefits beyond being able to anchor a POS. 5.0 or better standings with a faction will allow you to work for level 4 agents of any corp within that faction. Standing will also give you benefits in stations. High standing drops taxes, and broker fees in stations. Without high standings you will never refine anything at 100%, but with high standings and good skills, you can refine or reprocess anything at 100% efficiency.

Only corp and alliance members, though alliance is limited to jobs that don't require materials nor produce anything as they don't have hangar access.

A guide to POS labs

Really basic POS guide: EVE Online Player Owned Station (POS) Guide - PDF

EDIT: Note that POS = Player Owned Starbase (not station!).