I like many of the suggestions mentioned. It's always hard to pick only a few to really work on. I'm going to mention 5, but the order of training is negotiable.
1. Create ID. There isn't a much faster way to die than to get stuck in an ID with someone or something way stronger than you,and you can't get out. On the flip side, it would be nice to trap someone or something weaker in with you, or to be able to enter a locked ID, too. Also, it will eventually allow him to make them with a much wider selection of options, probably including time-warp ones.
2. Summon Elemental. It's clear that Gnome already has a good number of useful and probably powerful spells, including earth shield, at her disposal, and she's undoubtedly highly capable at fighting as well. While he'll need other kinds of elementals eventually, just working up one kind will make it much stronger, and it will increase his basic summoning ability which will help when he gets others.
3. Chunbu Breathing Technique. One can never be too good at basic, passive skill enhancement.
4. Bind. This is a ridiculously overpowered crowd-control ability. Who needs a wimpy snare when you can just completely immobilize them, possibly including magic, for an extended period of time? Even without modification, I would expect that he'll eventually be able to extend it to multiple targets on one shot, or to cover a wide area. A lifesaver.
5. Spinning Mana Arrow. Clearly, he needs other attacks, and elemental and exploding versions of this would be awesome, but this is clearly his main attack, and it should be as unstoppable as possible. In many games, a higher attack spell skill level makes the difference between an attack that pricks the skin and one that kills. He needs to be able to overcome as much resistance as possible, and more levels will probably help with that.
Although I made this list, it's clear that many others are needed. Skills such as healing, shielding, other damage spells(including, but not limited to, damage over time, elemental, area effect), buff and debuff spells, information spells, more summoning spells(elemental and other), crafting (including alchemy and enchantment), physical training, etc. need to be worked on. I suppose dish washing shouldn't be overlooked, either.