As mentioned above, every bit of advice I've read, says that for strobes you need a 'pure sine wave' inverter...not just a regular (cheaper) inverter. Although, that being said, I've yet to hear from someone who has ruined their strobes by not using a pure sine wave inverter.
I bought myself a PSW inverter and a small battery. This was before they has the Vagabond mini...and my set up is half the weight of the old Vagabond. But now, I would just go for the V.M.
http://www.thephotoforum.com/forum/photography-equipment-products/177686-ghetto-vagabond.html
I guess it boils down to how much power you'll need. If you need to fire several strobes, at full power, hundreds or thousands of time...then you'll need plenty of batteries or a generator/alternator.
But if you're just trying to fire one strobe a couple hundred times (maybe not at full power) then a small set up should be just fine.