To anchor a POS in high, your corporation needs a faction standing of 10 times the system's security level; eg to anchor a POS in a 0.7 system, your corp needs 7.0 faction standing . This is based on the sum of your corp member's raw faction standing before connections and similar skills. This is easiest to do with a single member corp, and invite other pilots after the POS is anchored.
I have done storyline missions before, based on the back of the occasional courier missions (mostly done afk), but most of my faction standing is from repeating career agents (6 sets of 5 missions), Keeping crimes in check and, so far L1 and L2 Cosmos missions.
This last week I started L3 Cosmos missions, and while I have spent an embarrassing amount of time reading how to fit a cruiser for PVE (some of the rooms are restricted to cruisers), the combat missions have been very easy. Anything that I can buy from market or contracts is bought, I have spent about 10M (and one trip to Jita) to get items / bodies / whatever the missions needed.
I used http://wiki.eveonline.com/en/wiki/Gallente_COSMOS_Guide to tell me where to go, what to buy and what to do.
I didn't do these missions to earn ISK, only to grind out faction standing. I have been surprised at the rewards for these missions, especially for the lack of risk.
I have salvaged nothing, looted nothing. I have gone into lowsec once (making sure that the station was not camped before docking there), and avoided the last L4 mission (it required entering the Contested Gallente Azure Chasm and purchase a 40M dogtag on contract). The last time I entered a contested area solo, I found the respawn time was shorter than my solo dps allowed, and the rooms refilled before I finished clearing them, corp mates were not on at the same time to help, and I got my required standing anyway.
Not including ISK rewards or some faction blueprint copies that I have not yet investigated how much they are worth, the mission rewards include :
- Yun Jung Technology skillbook (114M ISK)
- Passkey to Yan Jung Relic site (170M ISK via contract)
- Social Adaption Chip - Standard (22M ISK)
- Ocular Filter - Basic (10M ISK)
- 2 x 'Meditation' Medium Armor Repairer 1 (2 * 40M)
I used two different ships on these missions; a shield tanked Vexor (cruiser drone boat) and a Viator (Blockade Runner). Many other ships could be used, and if you can't use a viator, use any industrial the larger haulage missions, and a fast frigate (possibly with a scout) for the lowsec run.
You can also repeat the missions for your allied faction (Gallente/Minmatar or Caldari/Ammar) for additional primary faction rep (very roughly 1/2 of the standing increase).
It doesn't matter whether you are a merely working out a bit of faction standing to anchor a POS and reduce broker fees, or a mission runner looking for some easy ISK and a change of scenery, I recommend these missions.