Hi Pastor, I am currently working with a church that remarkably has a close resemblance of what you have, only they put down carpet tiles over a wood underlayment over a concrete floor below grade.
Sometimes us "pro's" get too technical on explaining things. You stated that you didnt know too much about this stuff. Neither does the pastor that I am working with. I know you will have to go through committees in order to get things done, BUT, the VERY FIRST THING you should do is get the whole group together and get ALL the flooring torn out of that facility, down to the base substrate which is probably concrete. The next thing to do BEFORE you decide on what type of flooring to use is do what a couple of people have suggested....do a moisture test. Let me tell you what this test does and why you need it. All concrete emits a MVER (moisture vapor emission rate). What that means is that water vapor is coming from whatever the dirt/fill material is under the concrete and the "earth" in general. This tests measure the amount of this vapor coming through the slab. Moisture is adhesive's worst enemy. It will make it turn back into a liquid if the amount of MVER is higher than what the adhesive can endure. Thus the flooring you choose will fail. Some types of floorings allow MVER to go through them, such as carpet, but being as unsanitary as it is, it wouldnt be a good choice for you. Here is a link to the type of test you should either have done,
Calcium Chloride Moisture Test Kit or if you think you can do it yourself, then buy the kits and do it yourself. You will need a digital gram scale to do it yourself. the results of the tests are measured in lbs./sq.ft. per 1000 sq. ft. in a 24 hr. period. Read through the instructions and see if you would feel comfortable doing it yourself.
I do synthetic sport flooring(s) for a living all across the usa and have been overseas as well. One other thing you may consider in the flooring you choose is: Are you going to paint any game-lines on the flooring you choose, such as awana square(s)? If so, there is specific paints made for specific floorings that you choose. I have done many awana games, all painted on. Have seen them taped on too, but I personally wont do that.
Floorcoverings have gotten so technical in their nature in the past years, that you need to be very careful in what you choose and why you choose it. Rubber, as you say you would like, would make a good flooring, and there are various installation methods to do them that would last a long time for you. There are various coatings you can put over the top of rubber to make them "not so absorbent" in their nature. You have to be VERY careful in the type of rubber you choose. There are a lot of rubber in the market today. Two types to look into, depending on your budget. Virgin and recycled. regycled rubber is basically old ground up car/truck/tractor tires. Dont get sucked into buying the cheapest rubber you can find. There are currently a lot of recycled rubber on the market that comes from overseas. These "cheap" rubber have chunks of wire still in them, some will make you room smell of old car tires, and some will fall apart after time. The virgin rubber would do you fine, and might even be THE CHOICE for you. Some of these can be "loose-laid" in that they dont require adhesive. There is always interlocking pvc tiles you can use as well with a rubber underlayment. If you want me to work with you on your project,
give me a shout at my email.
Good luck and God bless you. He will guide you through what you need to do if you just follow his lead.