Keeping a small number of kids is really important, especially if they don't interact much at preschool. Kids this age don't really "get" sitting around watching someone else open presents that they can't play with. And 4 year olds don't really "get" playing with others and not getting absorbed into their new toys 100%. So scale down your expectations. "See who comes" isn't a bad idea, depending on the number of kids you are looking at in total. We always followed the "age" rule - when our son was 5, he got to invite 5 kids. When he was 7, 7 invites.
Having a few kids that she knows well is more important than the class. Also, does the preschool have an in-class party with the parents bringing cupcakes or anything like that? That might be enough for her with these new friends. Invite a very small number of friends from her neighborhood/family circle if there are any - cousins, whatever.
Keep it simple with a few little games or a craft. Resist the pressure from others to do a big expensive extravaganza - it really gets out of hand, overstimulates the kids, and becomes a budget buster. At that point, it's not really about the kids.
Good luck!