I'd love to be able to set-up a playing history for myself, prior to starting a game. As it stands I can select a 'difficulty' level which defines how the players and fans react to me (Sunday League - International), but I'd love to be able to define which clubs I've represented previously, giving me a reputation with them prior, and building on that as their manager.
For example, I'd like to specify I - fictionally- played for Present North End between 1992 & 1995, making 3 appearances; probably quite a forgettable player and the fans would have no inclination to want me as a manager. In 1995 I made a 250k move to Leicester City and went on to play 130 times for them until 2002; chances are Leicester remember me and would potentially be inclined to have me back as a manager. In 2002 I made a £12m move to Liverpool and went on to retire there after 7 years making 205 appearances. In this final example I could be listed as a favourite or icon meaning home-grown players and fans would initially start with a warmer feeling towards me. Certain players would have been listed as a favourite as I played alongside them for a period of time, also, some would dislike me! I believe this would add greatly to immersion but it also leads nicely to be second suggestion.
I'd love if I could build from inside, like Pep at Barca. A former player turned 'reserves' coach who was raised from inside the club to manage the first team. I'd love to have the option of managing the youth squads individually and then, after loyalty and under the right circumstances, be offered a first-team role, either temporarily or full-time. If temporarily, do I now have bigger ambitions than reserve management? I would love to then be able to refuse returning to my previous post in search of top-league management. Along with this, regular conversations with the first-team manager to inquire which players are ready for the step up, or how I should have my squad playing to ensure a 'smooth transition' from reserves to first-team.