How much magnification can I expect from opera glasses?

Opera glasses are traditionally 3x25. This means 3x magnification and 25 millimeter-diameter objective. In other words, you will be able to see three times closer than wherever you are sitting.

What are some inclusions I should look for?

It's nice to have a built-in reading light in order to peruse the playbill. Also, look for things like an extendable handle and especially a necklace so you don't drop them. A carrying bag is also a nice touch for storing your glasses at home or in your purse or suit jacket.

What are the advantages to having a handle on the glasses?

If you want to use your glasses for the entire performance, which may be true when your seat is far from the stage, a handle is a good idea. The handle should extend, then you can easily rest your arm on your seat while looking through the lenses.