I did medieval history at university and studied this period.
Richard was a product of his time, ruthless certainly and able in Government but when you were one of the top nobles in a land which hade been in a state of civil war (on and off) for 100 years then these were qualities you had to have. His governorship of the North was generally thought to be good which is why he was well liked and respected in the Northern counties and had he got the luxury of time and been able to apply that leadership style on the national stage he would probably have gone down as a reasonably decent but somewhat unremarkable medieval monarch. The things he did manage to enact in two and a half years were pretty decent, putting England back in the black and reforming the justice system.
In terms of the princes in the tower, he probably did have them killed, there is also some evidence to suggest he had a hand in Henry VI murder as well. However, this was not unusual for monarchs and nobles at the time, Henry VII had the two strongest male claimants to the Yorkist line killed, one of them (the Earl of Warwick) would never have been a threat to him as he had learning difficulties and could never have been king. Indeed, if we look at other monarchs, Edward III had his own father killed in a very nasty way with a red hot poker, Henry IV had Richard II killed and these are not noted as being particularly tyranical - they are just a product of their times. At that time, England's governance was all out of balance with over mighty nobles and a relatively poor crown and someone always had their eyes on the crown or being the puppet master behind the throne - ruthlessness was just survival.
I dont really hold with the idea that Henry VII had the princes killed - he was certainly capable but I just dont see him having the opportunity and there is a lot of evidence that he would not have made the bid for the crown had Richard not usurped and caused a rift in the nobles.
Bosworth could very easily have gone the other way as most of the nobles held back to see who had the upper hand before committing. If it had gone the other way, Henry Tudor would not have been buried in any church but would most likely been quartered and sent to different parts of the Kingdom as a traitor.
But hey ho, that's history, it all turns on the roll of a dice and thats why I love the subject.
As for where he should be buried, being a Yorkshirewoman and not far from Middleham, my hear says York but in reality, Leicester is probably as good a place as any.