I think...if the spell is going to scale at all, then just do it by level.
It is most likely going to be damage (though possibly duration also) so a line in the spell description: "this spell does d6 per caster level" or "does 3d4 +d4 per caster level above X" is not really at all disruptive.
I DO like the idea of spells just getting more powerful as you go up in level, though...as opposed to "Silent Image, Minor Image, Major Image, Super Mega Major Image, etc. etc." or "Invisibility Rare, Invisibility Medium Rare, Invisibility Medium, blah blah". That just all seems unnecessary.
But at the same time I don't want to see spell lists that explain the spell and then beneath each description you have: Cast as the following slot...
1st: You turn yourself invisible for 1 hour +caster level (or Int bonus or whatever it might be).
2nd: As 1st but can now cast it on someone else.
3rd: You turn the recipient of the spell (either yourself or someone else) invisible for 24 hours without concentration.
4th: You can now turn anything you want within a 10' radius Invisible.
5th: Your invisibility is not longer dispelled by making an attack. Duration is auto 24 hours or until dismissed by the caster.
6th: wuteva wuteva
7th: moh wuteva
8th:...how many spell levels did they decide 5e was gonna have?
And then, you only have to do that, maybe, 100 times (out of the hundreds of spells in the various lists) for the spells that would be scaling. That's gonna amount to a looooooot of page count.
So, yeah, I think the scaling by level is a more practical choice from a lot of angles.
I also want to second the suggestion that "playing around with the spell"/ metamagic-esque should/could be tricks built into the caster classes that are gained as one increases in level/power. Extending durations, expanding range or speed of casting or doubling up damage, using it on an object instead of person or vice versa, etc... . So the spell itself doesn't change/have to change or be different...just how the caster is using it.
"Being 7th level, I can now cast an 'Extended' [the 'Range Extension' class feat/skill/whatever] Invisibility. That means I now make things invisible in a radius up to...30 feet. I'll hide every villager I can within 60 feet, centered on me, from the encroaching orc raiders." [or whatever it happens to be/however it works]
It's early...more coffee...I'll come back to this later after the babblerium subsides.

-SD