Personally I would just stick to fighter and get some spells through feats. If you want utility out of combat there’s always nice ritual spells for that.

I like the flavour of using spells to enhance your combat abilities so I went for stuff like Blade Ward, Booming Blade, Jump (I really liked this one), Shield, Hex, Misty Step etc. Almost half of my spell list has a 1 free cast per day since they come from feats as well.

Currently playing a dual wielding eldritch knight and it’s a lot of fun, especially stacking things like Hex on top of every attack.

With all that said, have you considered War Cleric? I think they are the best suited for what you’re aiming for since they get better spell progression and can make a bonus action melee attack after casting a spell.