Do you plan on continuing?
Edit: I've been doing some research for tommorow, and I'm not super thrilled with myself. Here's what I have so far.
Probably the closest place for us to play around in is Providence, so I would argue we just jump into there and start pew pewing. Here's the issue.
Providence is a very unique null sec region in that its proprietors, CVA, maintain what is called a NRDS (not red don't shoot) policy. This means that they don't attack neutrals on sight, which is pretty valuable for getting easy access to null sec resources. This also means that there are lots of carebear types in the region that present easier targets due to higher concentration. However, if we do attack someone in Providence we will end up on their KOS/Red list, and will be pretty heavily harrased in Providence, meaning that if we do want to do any ratting/mining in providence we won't be able to. Other than that though it won't be much different than going to any nullsec space.
There is also a chance that CVA won't be around much longer due to them getting face raped by AAA. Its an outside chance.
Anyways, the other option is for us to go to a different region. For this kind of operation its important for us to be near high sec so we can reship and jump right back into the gang. Right now I am leaning towards Syndicate. The closest high sec system to our entry system would be ~Yvelet. Problem is that that is ~20 jumps.
So here's the question. Do you want to move your ships to Stacmon (edit scratch that, yvelet), 20 jumps away, and run on Syndicate, or do you want to ruin your standings with CVA and go kill people in Providence?
Edit: By the way, that route to Yvelet is 90% low sec. That said its bar none the best way to get into Syndicate. The Orvolle gate is just suicide. And while Stacmon is high sec its isolated. This means that prices for everything may be a bit higher there. Good news is that it may not be a bad place for us to relocate to. Our industrialists will be able to make more money by supplying Syndicate, and the PvPers/PvEers will be able to do more with Syndicate right there.