A cycling shoe is an unpadded, stiff shoe that will fit in a size that is different than your running shoes. You need to order both, you’ll probably return both, and then order the right one in a better size.
XC501 - it’s a good starting point. Laces are stupid here. Boa is easiest to clean. The XC7 can be around the same price. Basically, just about everyone here has owned a Shimano shoe…and for good reason.
Giro - Recon over the Privateer.
Specialized Expert XC and Fizik Terra X5
If you have a narrow foot, you can find a lot of Mavic Crossmax’s on sale.
You don’t need an infinitely stiff shoe; just something that’s stiff from the mid-heel to the cleat.
It should feel like the perfect slipper - not needing to be tight to stay in place.
Size it by the arch and point sides of your forefoot hitting in the right spots as opposed to your toes being in the right spot, as the curve of the shoe is more important than the ultimate length - toes can have some extra room.
Get a shoe with two adjustments, not one. the lower one you’ll likely set once and never touch again.