With good scouting you can find a good keeper for not that much money. I'm not really for breaking the bank for someone, especially for Prem keepers. However if we are going to go that route.
Hart is good if you play a very defensive setup and maybe he can be obtained for a favorable loan deal. Playing 9 back isn't really my idea of happy fun everton though.
Schemichel's best attribute is starting a counter with those long throws and we are going to need an extra something in attack next year assuming Rom is gone. If he's allowed to do that I would be fine with him.
Pickford, he's young, probably decent, 15M isn't bad assuming he would probably stay here for a decade.
Also I watched a bunch of Leno as I did love watching Bayern matches this year. Their D was such a clown show that I don't know what to make of him.