Basement help - water and floors

[Susie]

Yesterday we got about 1.5" of rain in a short period, and at the same time, a 2-3 hour power failure caused our sump pump to go out.  We were at work, and didn't catch that in addition to being out during the outage, the sump pump didn't kick back on when the power returned (the float got stuck).  We came home to a 2-3" deep lake through the whole basement.  

We got the sump pump working again, got the water out, wet vac'ed the puddles, got rid of all the wet cardboard/etc., and have fans and dehumidifiers running.  The emergency has passed, I think we'll be ok.  The question becomes, how better to outfit the basement so this doesn't happen again, or if it does, it's not such an enormous deal.  We have lived here since 2008, and in that time we've had some minor water issues, but this is the first time it has made it to the "finished" side of the basement.  We can tell from water marks on the doors though that this happened at least once before we bought the house.

We've already done a french drain that diverts water away from the house.  That has decreased the reliance on the sump pump about as much as we can.  So the "what next" questions are limited to within the basement walls.

1.  Has anyone replaced an electric-powered sump pump with a venturi sump pump system that doesn't require power?  Did you do it as a backup, or as your main system?  Any advice on sump pumps generally?  (This isn't the first time our float has gotten stuck so it seems some change or improvement is due.)

2.  What would you do about flooring in the finished half?  The unfinished (back) half is storage, laundry, furnace, hot water heater, chest freezer, and a work bench, with sump pump in the rear corner, and I am fine with leaving this as plain concrete.  The front, finished(ish) half is a workout room.  The previous owners put in the white/pink flowered linoleum; I started ripping it out last night because I was grossed out by the thought of water being trapped between the linoleum and concrete, and mold growing.  I never liked it anyway so it was a good excuse.

I use foam tile for the workout area, so I don't need nice flooring.  I was thinking of either painting the concrete, or epoxy, or something like that?  I need to figure out how to accommodate the sewer connection in the floor, also.

PIPs:

Standing in each of the two doorways looking to the back half of the basement, sump pump and storage.
 

Finished/workout room side (high water mark on the door)




Concrete seems to be in decent shape under the linoleum.  The sewer main cleanup cap is to the left of the green bike trainer, and it sticks up above the floor.  When the linoleum was down, there was just a flap cut in it.  It was not an elegant solution.  I ran the foam tiles right over it, although it wasn't smooth.  I tried to put a bike trainer over it so no one stepped there.


Pre-flood:  this is basically what I'd like to get back to, except without linoleum under the foam tiles.  Solid, waterproof neutral floor would be ideal.