A character concept I came up with was a witch working off campus in a secondhand student furniture shop, complete with the basics. It's also how they can get ahold of odd items.
I definitely think you're on the money about cost, although I don't know that we want to plan too much about magic. My idea here is for the magic and fantastical elements to be a little like window dressing for a college town slice of life.
I like the idea of keeping the process of doing magic deliberately vague, since it's a tool for the narrative, and not the focus of it. But there's definitely a need to define some general rules and boundaries.
Like you say, any spell has a cost, and the cost must be paid for the spell to remain in effect. By the same token, I think we can hold with "equivalent exchange" as described in Fullmetal Alchemist.
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Maybe it's considered more like a private Ivy League school - difficult admissions process, requiring outstanding extracurricular activities/achievements or strong SAT/ACT/equivalent scores. It's divided a College of Theurgical and Thaumaturgical Arts which has additional requirements to get into (like how one might have to audition to get into a performing arts school, or need an impressive project on their resume to get into a technical institute) and has interdisciplinary studies within other traditional colleges, which were gradually incorporated in the 1800s/1900s as firearms industrialized, becoming more deadly and gaining equal, if not greater, footing against magic.
For the magic system, I think it makes sense for nothing to happen if you don't have enough materials - like in chemistry, when you don't have enough reagent for a reaction to continue. If you do something wrong, your magic can backfire, sometimes in improbable or bizarre ways, perhaps with even greater force than what your initial input was. A simple prank hex could become a harsh curse.
Maybe magic, like life, is just borrowed energy - as such no spell can last forever, and at some point it must decay and return its energy to nature. A magical contract can fade if it isn't "fed." Everyday enchantments need some kind of fuel to keep going - there are a variety of associated costs or sacrifices with them, but there's always a price to be paid, even if that price is trivial, silly (perhaps whimsical, even), or embraced with enthusiasm.
Edit: Also, if we're going for a 90's setting, I would love to bring in 90's music for character throwback songs.