I didn't see it mentioned but be cautious of buying bike parts online, especially Shimano stuff on Ebay, unless it's from a known seller as there are a lot of counterfeit parts being sold.
I started out on some Wellgo SPD pedals (like WPD801). They didn't have sealed bearings so I had to replace them every 5 years or so because stream crossings and mud would destroy the bearings pretty quickly. I disagree that the platform of the clipless pedal isn't important. After switching to Shimano XT pedals, I've found the bigger frame is beneficial for when I'm in repetitive, technical switch backs and need to step out going through the turn, I have something more to substantial to push against without having to clip back in.
I initially started out with some Nike "ACG" shoes with laces. They were a PITA because I was always either tightening or loosening the laces (or getting them wrapped up around the pedals

) trying to get them comfortable and the soles weren't stiff enough to really get the benefit of power transfer and stability. Because the cleat was recessed, they were good for hike-a-bike and walking, I actually wore them all day at work a couple times because I'd forgot to bring a pair of shoes to change into (i used them for commuting to work too). But they were hard to clip in/out because the cleat was recessed and, if it was muddy, I'd have to clean that area out with a stick before I could clip in again.
Go to a bike shop or REI, etc., and buy your shoes. At REI, I was able to try on many different pairs and ended up choosing some super ugly Shimano shoes (can't find a model number on mine but they look like the women's SH-WM53 version) because they fit great and had simple velcro straps. I bought those in 2015 and am still using them today. They've held up great getting covered in snow, mud, drenched in water crossings. I just hose them off after the ride if they're dirty. They were cheap too, around $80 if I recall correctly. Only negatives are they're not very comfortable to walk in and pretty sketchy when trying to climb up rock because of the hard plastic/psuedo rubber soles and the cleat isn't recessed much, but the comfort while on the bike, super stiff soles, and ease to clip in/out far outweigh the negatives. The tops are ventilated so 20 degrees F is about my limit in them for cold weather riding. I appreciate people posting what they're using in cold weather temps, I'll have to check those out.