I'd also look into LTO (lithium titanate oxide) if you're interested in long term cost per KWh, not because they are cheap by any means but because they (allegedly) last so long that you'd only be able to replace them maybe twice over your lifetime, it's a pretty new chemistry so unfortunately it's rather early days to verify whether any of the consumer offerings available today will actually perform for as long as the companies manufacturing them suggest (I've seen figures quoted everywhere between 5000 and 30000 cycles at 70% DoD), or whether you could even take advantage of those kinds of cycle counts before the cells just died from calendar ageing.
Back to NiFe though, you can certainly get decades of use comfortably out of NiFe cells, but it's worth taking into account that they require a lot of maintenance, routinely topping up each cell with deionized water (there are automated systems you can buy or build yourself to manage this though), and every few years the KOH electrolyte inside them will need replacing every few years, plus you will want to keep your cells adequately ventilated as they vent hydrogen periodically.
I would definitely NOT recommend lead-acid, sure the upfront cost is lower than anything else by quite a ways, but they won't last long at all, and as a result I'd be surprised if you weren't paying a lot more in the long run.