What type of glue would be best?

Are the pearls going directly on the shoe or the lace?

If it's going right on the shoe then I believe E6000 glue might work best.

For the lace, .... I don't know what it's called, but it's a can of spray glue that works for fabrics.

The pearls would be glued on over top of the lace. So just spray adhesive? Thats simple enough

Spray adhesive was not enough (I glued lace appliques to my shoes) for me. I did it early, and when I took my shoes to my fittings the lace started coming off. I got some super craft glue that comes out clear, and re-glued with that, and it's solid now. I can look up the label if you like?

Second e600.

I've been using a Fix-All Adhesive made by Super Glue that's clear and really strong, and dries really quick. I've been using it to hold down the ribbons on my bouquets and bouts, since they're all artificial, and I didn't like the look of the pins in the ribbons. It's really strong and rubbery, and I think you could get a pretty good hold if you only used it around the outer edges where the borders of the lace contact the shoe as long as it's kept taught while you glue it.

I'm going to attempt something similar. I'm following a blog I found earlier that put tulle on the shoe first then attached lace and rhinestones. They used Aleene's Tacky Glue then sealed it with ModPodge.