Your shelter sounds like it would be great! I have a "shed row barn" which is essentially a row of stalls that open directly out into my paddock. I was going to just build a run in shed, but we get big cats and coyotees etc. in my area, and that worried me. I enclosed the front half of my stalls with plywood, (mine are 8x12, but 8x10 would have been big enough) then the other half is a plywood stall door, made as dutch doors, the top portion is a framed piece of "cattle panel" which is a rugged wire "fence" panel with 6"x6" squares. We cut it to size, framed it with 2x4 lumber, and hung it. During the day my door can be kept open so they can come and go in the stalls as they please, but at night I do put them in with the doors shut incase any predators might come out. I like the cattle panel opposed to a solid door, it still lets them see outside and get fresh air, but will keep coyotees, stray dogs, etc out.
As a new horse owner, you will want to find a reputable vet, and maybe even have them out just to do a wellness check. We have our vet out twice a year routinely for shots, and then for emergencys or illness. He looks healthy in his pictures, but its always good to meet your vet and get a feel for them before you need them in an emergency. Its also good to build a "relationship" with them, because it will make them more likely to answer the phone when you call at midnight with an emergency, lol.
You'll also want to find a farrier, and have his hooves trimmed about every 6 weeks.
Deworming generally every 8 weeks, but you can also do fecal egg counts beforehand to see if he needs wormed beforehand. Many people just deworm on a set schedule. Sadly, the wormer is MUCH cheaper than the egg counts. The eggs counts cost me $25, the wormer I can find on sale under $3.
Research "Colic" and be familiar with the signs, it is a "common" horse ailment, and can range from mild to deadly. Your better to catch it early, but if you havent seen a horse colic, its easy to miss the first signs.
Get some first aid supplies on hand. You can buy premade horse first aid kits, but honestly, most of the stuff in the premade ones isnt stuff you need, and they forget the important stuff. Its easier to just put the kit together yourself. Ask your vet for a tube of banamine to keep on hand to use in emergency incase you need it before they get there.
Get some books from your local library on horse care, or look around the internet. There is a TON to learn, but its a great adventure. Do you have a local horse facility where you could get lessons on horse care and they could help you learn horse body language? That would be a huge help