This page has suggestions about where to get the sheet music you need. Please let me know if you know of other sites that should be on this list!
Petrucci Music Library
This incredible online catalog of music offers a huge selection of classical music for free. Most public domain music in the standard repertoire is included here. If the piece you’re looking for is part of a collection or a larger piece (such as an opera) you will need to know its source to find it here. Art songs may not be available in the keys you need. You can download pieces in PDF format.
Sheet Music Plus
Sheet Music Plus offers a huge catalog of (hard copy) sheet music you can order. It also does the tremendous service of actually listing on the site which songs are in a particular book. They do tend to have higher prices than some other retailers. That said, I like their site and I like to support a business that specializes in music, so if I have a couple bucks to spare I shop there anyway.
Amazon.com
Amazon is the go-to place for sheet music at the most affordable prices. Before you go there, though, find out exactly what you’re looking for and search by ISBN if possible. Many books look very similar but have different content (e.g., Hal Leonard releases books called “Standard Vocal Literature” in soprano, mezzo-soprano, tenor, and baritone versions). Amazon doesn’t list the selections in its product description, so unless the book has a “look inside” feature, you may have to do your due diligence elsewhere. It can also be hard to tell whether a book includes a companion practice CD (I don’t recommend buying books without a CD unless you don’t have a viable alternative).
MusicNotes.com
MusicNotes is a great source for downloadable pop and, I think, musical theater sheet music. They sell songs individually for about $4 each. If you’re my student, you probably already know how important I think it is for pop singers to have charts to read.