One point on shoes with cleats - installing the cleats is easy, positioning them right is important.

You can find lots of YouTube videos around doing this, but if you are looking at buying shoes from a bike shop ask them if they will do a cleat fitting for you if you buy the shoes from them. Needs to be a bike shop you do have confidence in - many bike shops are clueless around fitting other than having the top tube and seat height line up against your legs/hips. Even if they charge for a shoe fitting, once you have it dialed in on your shoes you'll be able to transfer the same alignment to any shoes you buy in the future pretty easily.

I did trail and error positioning when I first went clipless and thought I had it dialed in pretty well. Three years ago I bought a new bike that came with a discounted fitting and the fitter (who wasn't a bike shop salesperson or mechanic - he was a sports physical therapist who did fittings in the shop in the evenings after work) moved my cleats back in the shoe all the way. (he also raised my seat almost 3/4 of an inch and took out the tilt down. On longs ride after that, I was impressed on how much better my knees felt.

I started with SPD (two hole cleats, like your wife's spin bike) and use those for over 10 years. When they were still usable (Shimano) I bought a pair of SPD-SL (three hole cleats) shoes and tried those out. I liked the connection to the pedal much better but walking in them is a pain and if you walk too much the plastic cleats wear out and they aren't cheap. I now have SPD on one bike (what today would be called a gravel bike) where I am more likely to be doing walking and SPD-SL on my road bike I use on long rides or just exercise rides where I won't be doing much walking. And I still use the original Shimano SPD leather lace up SPD shoes when I do indoor spin classes in the winter!