You don’t want ones that are too small and pinching your feet, of course, but your feet sliding around in oversized ones can cause issues too.
There are a few things you’ll want to avoid at Everest Base Camp: flip-flops, uncomfortable hiking boots, and cotton clothing. While flip-flops are usually a good choice for “camp shoes” under normal circumstances, this isn’t one of them. Even in the lodgings along the way, your feet are likely to get cold and certainly will if you’re staying in a tent. You’ll also want to break in any hiking boots ahead of time and make sure they fit correctly. You don’t want ones that are too small and pinching your feet, of course, but your feet sliding around in oversized ones can cause issues too. Last, there is a saying in the hiking world: cotton kills. When cotton becomes damp, it clings to the skin and can take a long time to dry out, neither of which will lead to anything good happening on this trek. Save your favorite cotton t-shirt for sleeping in.