Good Morning ,
I have had shed roof issues ,I finished up using box profile insulated metal from a company called Steadmans thy have all the requirements to complete the job ,the shed will fall apart before the roof gives in .If the wood under the felt is good "ie"thick external ply and not boards self adhesive tiles are good thy come in a strip of 4or5 thy look good when finished and easier to handle, you do not say if it is a peak roof or a pent roof ,if it is pent the tiles might not be my first choice . As to the question about rubber type felt I have never used it because I wanted to do the roof once and for all , and again it all comes down to budget. That's my input for what its worth .
David