Hi,
Just because a band has a saxophone or double bass doesn't necessarily mean that they play Jazz. . For me a band playing jazz needs to do some solo improvisation.

Back to the topic, if you plan on engaging a live band for your wedding, apart from the price negotiation, you need to do the following.

1. Audition the band. See if you like what you hear. Also, confirm that the musicians playing are the same ones you will be seeing play on your wedding. There are some bands which just swap players around as they have a group of musicians. Problems is, that they use the more experience players for the audition & for the actual event, they send the junior ones so the bands sounds different.
2. Prepare a time table showing the event schedule during the event & show when the band plays so they can schedule their sets as well. Also, let them know what time they can come in to set up & sound check.

3. Consider using a third party sound equipment supplier instead of the hotels. You may pay a little more but at the least the equipment would be working. Some of the hotel equipment I've seen are not useable & badly balanced.

4. Decide on what kind of music you want played. Jazz, classical or contemporary ect & select a group that plays it well.

Hope this helps.