I'd say the best relationship with one of the faction contacts is a professional one. If you have something useful to offer to the faction, you'll have a good time talking to them. Waste their time with idle chit-chat or semi-useful fluff and you won't get much in return. Aldy has mailed one of the contacts on orders from his CEO with a particular goal (forming solid bonds of communication with useful individuals) in mind.
Remember, these contacts are there to facilitate live events and to help direct faction-aligned corps influence the story line through in-game action. They're not going to be doing /sip RP, this is srs bsns blow shit up RP. If you're not going to be in that or be helping that, don't bother, I suppose.