POP Email Accounts & Change DSN Settings, broadband install

Website is due to be directed to a new hosting company where a shopping cart is in place. Webmail may possibly be kept with old host (preferrable) depending on necessary info from new, or new pop email boxes set up with new as they do not offer web based email. Many pictures received and sent by email so need a robust solution. Also if email is to be recieved using POP, we need a system whereby it can be forwarded but still answered using our domain emails from other locations, so recommendation and set up of this is required too.