The basic requirement was that they be offensive and targeted spells; I had no desire to try and adjudicate sword-heals or dropping a summon spell with the sword attack. The main spells he used were Chill Touch, Fire Bolt, Ray of Enfeeblement, Bane, Shatter, and Vampiric Touch.
The closest thing to a general rule I had was that the spell had to be an action. The actual action was Cast a Spell, so it didn't trigger any Attack action required mechanics. They had to use one specific enchanted blade, so the attack couldn't be swapped for a shove or grapple or anything like that. They would make the attack first, roll damage, and then the spell would fire, even if the target was no longer valid (attacks could be retargeted if the melee attack target died, though, like in the case of Scorching Ray).
For spell attacks, the melee attack replaced the spell attack roll. If the weapon hit, the spell also hit. If the weapon missed, so did the spell. Area effects were centered on the melee target, and the caster was immune to the spell's effect. If the weapon attack missed the target, that target only would have advantage on a save if the spell required a saving throw.
Cantrips used replaced on of their damage die with weapon attack damage, fire bolt did 1d8 fire + the weapon damage at 5th level, for example. For cantrips in Tier 1, they were really only useful for the rider effect.