They have level one missions just like in highsec. All the level 1 and 2 can be done in a frigate. Many level 3’s can be as well. Also you can do level 4 team burner missions even in a cheap Tristan if your pilot it well. (That’s how I started doing burners myself). Imagine making billions with a Tristan lol.
Anyhow if it’s missions your after, even in null sp is not an issue. Learning to pilot your ship well is handy though.
Don’t kill other faction ships ‘just because’. If you end up in an anti-faction mission, google it, kill the absolute minimum to complete, get out.
Click on the faction icon beside the goal/objective when offered the mission (or just look at it). If it’s someone you don’t want to take a hit against, decline.
Find a station or system with multiple agents in it. Then if you have to decline some you can still check the others without flying 8 jumps.
You can run a set of Career Agents for any faction (probably listed in that Faction Standings Repair Plan link). Every Career agent that you complete will give you a decent boost with his faction.
If you run your standings down with faction X, then go run missions for X for a while and do their dirty work. Your gains are bigger than your losses so you can stay positive by alternating factions. (2 steps forward, 1 step back is still 1 step ahead)
Like @Wadiest_Yong suggested, check out ‘The Plan’. It’s actually the easiest and fastest way to repair / raise Faction standings.
No question that a major mission overhaul is needed, but CCP has always said “it’s good enough.”
Doubly frustrating when assigned a mission to aid an opposing faction by supplying medicine, heaters, life support, or transporting their citizens from their faction owned station to save them and then get dinged in your standing with them because you aided them. 
Would like to have some common sense applied and have a few storyline missions where actually helping people or destroying universal enemies (rogue drones) would not create a faction standing loss. Too bad common sense appears to be another asset in short supply at CCP.
So, @Robert_Cras …the solution to your question was presented…Did you check out the Faction Standings Repair Plan?
Of course it should.
A and B are enemies. You are helping A, so B thinks of you less.
The fact of accepting a mission should not generate a standing loss, however.
And, in general, gains are bigger than losses (for storylines, at least), so if you keep tabs on your standings and change up who you do missions for, accordingly, you can keep all of them in a reasonable range.
Also, I just noticed this the other day, as I’m doing my first ever empire epic (so, not including SoE here). I have high Amarr and Caldari standings, and I’m in the middle of doing the Amarr epic. When I looked at the Agency tab which shows the epics (I’d never looked at it before), it indicated I was eligible for Amarr, Caldari, and Gallente. The Gallente surprised me, because I had just done my first ever faction repairing, specifically for Gallente, and had raised it up from -3.something to -1.6. So, how was I eligible for the epic, since I’m a long way off from 5.0?
Turns out, the epics are available with 5.0 standing for the empire, or one particular corp in that empire. For Gallente, that corp happens to be the one I used to work on Gallente standing (by accident, I just got lucky).
So, you don’t have to keep everybody at 5.0 for access to the epics. Just above -5.0, and then 5.0 with a certain corp, and those don’t go down from derived standings, so you’re good to go.
You’re correct about having +5.00 standing with the Corporation of the starting Agent for the Epic Arc. However, the Faction standing needs to remain above -2.00 standing to maintain access to Agents above level 1.
I know derived standing… but that’s just a little you go down or up with other factions… this was down 0.48 in total in 1 mission.
I did!!
Standing changes for gains/losses towards npc’s are larger in the beginning, that’s how the formula works. You can find it at https://support.eveonline.com/hc/en-us/articles/203217152-Standings if you’re interested. It does not show any base values (how much for killing a ship, or a structure) or even based on what exactly.
As an aside, the standings interdependency matrix (who likes/dislikes who and by what increments) only comes into play when doing storyline missions. That’s why I wrote earlier that it is very time consuming or difficult to have positive standing with the four factions. You CAN use The Plan to do it. Most people are happy with not dropping standings below -2, just for the simple comforts of traveling and not having faction police on your tail all the time. When they need access to racially “restricted” stuff, like certain hard to find RnD missions they probably use alts.
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