Edit: Regarding shoe/pedal combinations. Sidi shoes if they will fit you otherwise I'd go with Specialized. The BOA fasteners are really good - crazy durable, easy, they stay, can be replaced etc. no downside except upfront cost maybe. I really like SPD pedals - Shimano XT in particular. The lower models have a plastic part that will wear and the bearings go sooner. XTR pedals cost a fortune for no durability gain and it's a spin bike so not going anywhere.
But yeah, my wife and I already had SPD shoes from doing spin together for awhile, so I bought pedals and never used the ones that came with the Peloton.
Top three brands off the top of my head:
1. Bontrager: Owned by Trek, and is the most common type of spin shoe used in studios. Will have something for all price ranges, and have been around for a while.
2. Specialized: More ubiquitous in the cycling world, a slight amount of paying for the brand, but will also have everything you need. Most popular cycling brand, especially on the high end.
3. Fizik: Personal favorite because they are better for high arches out of the box. Unlike the other two, these guys don't make bikes, just shoes and seats. And they do both extremely well.
I HIGHLY RECOMMEND going to a bike shop to buy the shoes and have the cleats fitted to your shoe in-person. This prevents injuries and improves results on the bike.
Pay for in-store once, take a silver sharpie, outline where the cleat is placed on the bottom of the shoe. Now you can replace the cleats for $20, and have a good idea of where to place them if/when you need a new pair of shoes.
If you have narrow or low-volume feet, the Italian brands might work best.