@BulldogBride: It’s actually not so much about choosing songs for your wedding. You can get by with just having an organist for the procession, recession and communion. The thing you’d need a singer for are for the parts of the Mass that are called “The Propers” These are prayers that are typically sung on special occassions like weddings.
Generally speaking, this gives a pretty good guide over where you’d need music: In regard to what you’ll need for your wedding, I’d start with this site: http://catholicweddinghelp.com/topics/order-wedding-with-mass.htm
That said, if you want your Mass to be really elevated, it is entirely possible to sing nearly the entire Mass. The wedding I was just at last weekend had the priest chanting the entire gospel. They usually only do this at big events at the Vatican, however, and not all priests are great singers.
To give you some guidence on the type of music that is appropriate for Mass, I recommend this video: http://www.youtube.com/watch?v=9XTHFbM4ZFM
I’ll try to divide these between what you’d need a singer for and what you could get by with just an organist.
Entrance — organist is fine. Most parishes don’t allow you to use recorded music.
Gloria — This is a prayer that can be sung, so a singer or singers would be appropriate.
Here is the classic Latin rendition of the prayer: http://www.youtube.com/watch?v=aUIPnmOrxFk
If you want something in English that is appropriate and easy to learn, try these
This will give you some comparison.
Alleluia — it has two parts. First there is the praise of “Alleluia”, but then there is typically a short quote from the bible. Its typically one line. Georgian chant is made to have the words fit the music. With modern music, the music has to be made to fit the music. Thus it limits your choices and forces you to find an Allelulia that already has the music fitting to the quote you want. A lot of times musicians make slight changes to the words to get the idea to fit their music.
Here’s an example of how the Georgian chant tradition allows for any quote: https://www.youtube.com/watch?v=d1GChkZYUVw
The versus of Responsorial psalms often work the way described above as well.
Presentation of the Gifts — you could pick out a hymn or just have organ music
Sanctus — The Latin version most people are familiar with https://www.youtube.com/watch?v=BxZobRDmVDc
Same sort of melody with new English translation: https://www.youtube.com/watch?v=6RD4uRSWY_A
Great Amen – https://www.youtube.com/watch?v=oHUHH2Mouc8
Lamb of God — This is the classical latin notes, but put to English https://www.youtube.com/watch?v=6s0m-ecaDFI
Communion — you’re fine with just organ music
Recessional — Usually you want something that has a tone of rejoicing in it. It can be organ music.
That said, you will have to work with the limitations of whoever you get to sing. Typically the parish will allow you to hire members of the parish chior. These people typically do multiple Masses and have stacks of music they’re familiar with that they might recommend you. If you bring someone else in, that person should be familiar with the parts of the Mass. I wouldn’t recommend using someone who has no experience singing for a Mass.