Behavior is like this:
- Sync: mail items stay on server
- Delete on phone: mail item removed from server
- Delete on server: mail item removed from phone
So don't worry about mail being removed due to syncing. Set your PC web client to remove mail after 2-3 weeks though so your inbox doesn't overflow.
Any way you can migrate the mailbox to Exchange? That requires less data traffic and allows for real-time syncing
Regards and enjoy your new phone,