Whatever you have in your closet that you would wear were you to be introduced to the president of the United States and the Queen of England at the same time. Wear that.
It’s more common than not, in my experience, for women to veil themselves or wear hats at the TLM. It’s really up to her though. There are generally veils to borrow.
As with every other Catholic Mass, stand when they stand, sit when they sit.
Usually they have little paper missals you can use for the day. The Latin Mass is much different, much quieter, than the Novus Ordo. Don’t expect to hear everything that the Priest says; the Latin Mass is more contemplative and medatative than the Novus Ordo in that way. It usually takes people a few times to get used to it. Lots of people are new to the Mass, and we’re always glad to have newcomers, so nobody will be watching to make sure you know every genuflection.Oh, enjoy!
Your wife would be fine in a veil or hat. Just wear church clothes: tie and jacket, a dress or skirt and blouse for your wife.Regarding dress, for me, where I go it’s maybe 50% in a suit or at least a tie. As for me, I’ve been wearing a nice polo shirt, khakies, and Birkenstocks (sandals). Nothing wrong with that either! Just look nice.