Hawk Diesel
Adventurer
I suggest something a little more radical. Instead of having set spell slots, have spell slots come on line when you hit something with a melee weapon: 1 hit lets you cast a cantrip once, if you make 2 hits and don't cast a cantrip, you can cast a 1st level spell once, etc. (spells need to be cast before you complete a short or long rest). The maximum level of spell you can cast should be equal to a wizard's at the same level. I would link it to a full caster rather than a half caster, because you aren't going to be casting spells that often compared to either full or half casters. Even assuming the class eventually makes two attacks a round, that is still 5 rounds of combat before you cast a 9th level spell.
This leads to an interesting gimmick for subclasses: each could provide something different magicwise for you to do before you hit something (preferably to better enable you to hit something and to survive the experience).
In my mind, this is the best gish because it makes both the fighter part and the mage part important. It also means this class would shine in hard slogs--when the other casters have ran out of spell slots and reduced to cantrips and regular weapon attacks, this PC is hitting his/her stride.
Now see, that's the kind of interesting an unique mechanic that a core class can be built around! If you are to go that route, I would probably allow the class to get Extra Attacks equivalent to a fighter. This would allow a for the mechanic to have a natural way to progress, so that you are not having to wait multiple rounds or multiple combats at high levels just to get a 5th+ level spell off. The other alternative would be increasing the level of the spell an attack starts with and adding one spell level from there. I.E. at first level your first hit allows you to gain a 1st level spell slot, with subsequent growing the spell slot by one step; at 5th level your first hit allows you to get a 2nd level spell slot, with subsequent hits increasing the slot by one step, ect.
That would actually be a really interesting class.
EDIT: The only problem I can see potentially is how you define an eligible target for the attack. I could see this leading to a new "bag of rats" problem where between combats this character would constantly have a horde of small, low CR critters to kill and refill spell slots.