If it is just for storing your yard tools, then a single four foot, two bulb fluorescent or LED shop light would work fine mounted in the center of the ceiling.
That is what I have in my 10'x16' shed. It has just enough light so I can see everything when it is dark. I have an LED four foot shop light in there so that even in the wintertime when it is cold/freezing it will light up.
I had a four foot fluorescent shop light that worked great, but if the temperature got below freezing it would take longer for it to get bright than the amount of time I was just going in and out of the shed to get a snow shovel or whatever.
As for lumen output, that all depends on you. The older people get the more light their eyes require to see. The LED shop light that I have says it puts out 5000 lumens, and I can tell that it is much brighter than the old fluorescent shop light it replaced, even after I put new fluorescent bulbs in it.
Jim