There is often a big difference in selling price if a player is already coveted by another club as opposed to simply listing them as unneeded and trying to flog them. Not to say that latter won't get you any value - it may, but its not as likely.
I've started with Bournemouth a few times and every single time, Liverpoool want Max Gradel and make an offer almost immediately. The offer is usually around 14m euros, just under his value. I've managed to negotiate them up to just over 40m Euros total. 20m up front, between 15m to 18m over 12 months and then a few million more in clauses. That provides a ton of to play with, but Bournemouth have one of the lowest reputations in the EPL so you may not land the kind of players you covet.
Burnley - Michael Keane is always wanted
Everton - pretty big transfer fund to begin with, Mirallas, Deulofeu, Lukaku and Barkley are always wanted
Southampton - reading anyone's experiences with Southampton, their stars are constantly raided
West Brom - Dawson and Berahino are often wanted