Paltrow as Margot is the first long-lasting celebrity crush I had as a kid. It was so long-lasting that it's still happening today!
Britney Spears was first in general, though. The media I consumed as a kid didn't have many women in it in general, but Britney was unavoidable. She was the first girl Iever liked in that way, but it lasted for, like, a day before I went back to hunting for a Dratini or whatever.
Other ones that come to mind from around the same time: Emma Watson (as Hermione), Alannis Morissette (as God in Dogma), and (for animated characters) Buttercup from the Powerpuff Girls.