I got no problem with each skill being learnable, but with the standard system, if I give out enough points to make multiple spells possible the non-magicians get a bit too powerful.

But you're right, so let's give an overview of the magic system. I'm trying my hands on a Novus conversion of Germany's "Dark Eye" system, to sell it to my players. Said system has grown with every edition and currently looks like a bloated cross between WFRP and GURPS (point-based, professions, lots of skills). Currently we're running a HERO conversion of that, and with all the house rules and customer powers, it looks a lot like Novus, just with a more needlessly complicated spell construction system

Academy of Mental Puissance:
Core spells (7): Charm Person +7, Dispel Charms +5, Cause Fear +7, Leech Mana +4, Hold Person +6, Compel Truth +6, Sleep +7
Other spells (14): Analyze Magic +2, Boost Stats +2, Constrain Movement +3, Telepathy +2, Blast +3, Hallucination +2, Dominate Person +4, Cure Poison +2, Change Memory +2, Detect Magic +4, Exorcism +4, Blur Memory +2, Mass Fear +2, Repulsion +2

So 21 spells that are known to most students. For context, you also get 37 other skills, languages and scripts. With Novus skills being much more coarsely grained, there's simply no balance here. Although that might be another solution, just bloat the skill list a bit to provide some balance. This is definitely a setting where a lore skill or a language isn't considered wasted.

There are two things I like about this and that I wouldn't mind to carry over into a conversion: Mages know a wide variety of spells and aren't equally proficient with each. So bonus points for any system which lets me keep it that way. And where it doesn't take countless hours and/or fiat judgements to convert the actual spells (Novus really wins here already.).

For my HERO conversion, I settled with "free" spells, so the PCs don't have to buy them as powers. Between the other guys getting "killing attacks" via their equipment, the cost of the mana pool and all the skills required it balances out quite well.
So every spell is a skill. By generally reducing the cost of skills in this HERO campaign and HERO's "skill bonus" mechanism (e.g. "+2 to all divination spells"), this works out pretty well. The spread between minimum and optimum ability isn't that high, though. It looks a lot like GURPS magery in play, where you try to get your INT and Magery high enough so that you just have to buy each spell for 1 (or 1/2) points, maybe with some additional emphasis on the spells that are really hard to cast.

So for Novus, I'm okay with not being able to model that every spell has its own level of mastery. If at all necessary, I can always create basic and advanced versions of the same spell. Avoiding instant mastery for any spell that you just learned is a nice feature, but not entirely necessary. Given that training time wasn't stringently enforced in the original, given enough experience points you could ramp that up unrealistically fast anyways. But I'm reluctant to part with the sheer amount of spells.

Although it seems that Novus' starting power level actually might be closer to the D&D idiom, and other games aren't quite that much zero to hero. So a few extra points at the beginning might not hurt.

So the "don't attack rule" is already in play? I didn't realize that, it wasn't mentioned in the spell base and just appears in the main book at a few specific places (e.g. the cloak and gremlins). In that case, I'll probably just going to replace that with the "only in the buff" modifier. It's a bit more difficult when it comes to the same when shapeshifting. It's a disadvantage if you're shifting yourself, but an advantage when transforming others (you can loot the stuff of the guy you turned into a frog).

Anyway, thanks for the long answer. I'm starting my conversion and will probably get back here with further questions or the results

Let's say my setting has a lot of spells. Even beginning mages might know about 20 of them good enough to cast them. I can simulate this a bit by just making the lesser known ones weak enough so that they cost very little (once the players knows them better, they can "upgrade" them to more powerful ones). And of course I can give out more points to everyone at character creation.

But are there any other ideas about this? Cheaper spells if bought as a package? Spells given for free, but the cost used as the base of a casting penalty (cf. HERO)? Free spells but multiple casting skills (one per spell a la GURPS is probably out of the question given the cost structure and the lack of "Magery", but maybe one per "school" of magic?)?