THis is really not difficult at all.

Your pedals are SPD pedals. Go to any bike store or on line and buy Shimano SPD cleats. They'll cost about $15-20 or so. There are totally compitable cleats made by other companies that are a little cheaper, but some are similar but not compatible. Therefore, for a beginner, just buy Shimano brand.

Then buy any shoe that is compatible with "2 hole" or "SPD type" cleats. This means SPD, not SPD-SL, or SPD-R. All shoe descriptions will specify this if it is true for that shoe.

Any mountain bike shoe will work. Most (all?) shoes marketed as "touring" shoes will work. Many "road" shoes will work, but you just have to make sure they specify they work with the "2 hole" or "SPD type" cleat.

My recommendation is to buy shoes locally to ensure comfortable fit. That is WELL worth the extra 0-25% you might save mail order. Fit is EVERYTHING. Buy the best fitting best quality shoes you can afford. Buying locally will also ensure you get the right shoes for those pedals, although like I said, it's not complicated at all.

My recommendation is also to go with a mountain bike type shoe at least to start. They're much easier to walk around in and have no meaningful downside at all. I've ridden road bikes with mountain bike pedals and shoes for 15 years now. I had "road" shoes once, but never liked them and they provided no advantage to me.