I'll chuck in my 800 m swimming badge and raise you a Cycling Proficiency.
No, I do not consider a state funeral would be appropriate. The point of a funeral is for those who are living to remember the contemporary dead. However, if the remains are RIII's he should be reburied with the reverence that ought to be afforded to a long dead monarch (he is not after all a recently deceased member of royalty and given that he died in 1485, no one could really mourn him with any seriousness - and by that i mean in an emotional way not in a nationalistic way) . I agree York may well be a suitable resting place given that is where he was loved. but given he has (if it is him) been in Leicester for nigh on 530 years, what's wrong with a suitable tomb there? It may not be thought of a royal stronghold now but in the 14th and 15th century it was an important town. THe castle was a regular seat of Royalty and the Dukes of Lancaster.