In a former life I did flooring as a full time job. I'd done a couple church basement kitchens and always recommended a material called VCT tile, comes in 12" squares. It's designed for industrial application so it wears well, not as slippery as sheet vinyl and is cheap. It does take some practice to put down though. You need a heat gun and a vinyl tile cutter (It looks like a paper cutter and you can rent them). About the only prerequisite for the base floor is that it be very clean and relatively smooth.
You lay out the floor, spread the glue over part of the floor, let the glue get tacky, and then set the tile. The glue will stay tacky overnight so you don’t have to lay all the tile the first day. Once it’s down the tile needs to be rolled and polished.
I’d offer a hand but I don’t have the time and I sold my tools for that trade before moving out here. With a little practice it’s not beyond what weekend warrior could do. Hope that's at least some help!
You should also mention though that to maintain VCT truly it needs to be cleaned and waxed often; at least yearly.
He is right though, I would say a VCT is the best and you can always find someone to install them. VCT is what you see on the floor of every Targe, Walmart, Kings, Safeway, etc.... The basic VCT are cheap but, as with so many things, do not go cheap. Go for the most you can afford and it will be worth it.
VCT install is quite easy but remember (course you are not installing it yourself) that the glue has to "tack" before you install. That means it dries for 20-30 mins and then the VCT is installed (like tile) and then you need to roll it; a 100lb roller over the area.
One great thing about VCT is you can get a low VOC glue (for stink) and you can install areas at a time so the entire area can still be used. Do remember to protect the edges though.
I can go on so I will quit... you can PM me if you would like or post a Q.
Other suggestions for a church floor:
Cannot go wrong with good commerical carpet (added warmth too)
Real commerial vinyl (not the loose lay stuff)
Newer vinyl tiles ($$)
Commerical porcelin tile ($$$)
Painted concrete (never been a fan though)