I cannot imagine anyone with insurance that doesn't want you wearing a helmet while you ride. Here is the most affordable one on the market: Horse Supplies, Dewormers, Equine Supplements & Tack - Horse.com
If you fall and crack the helmet you REPLACE IT. ~$25.00 is a good insurance against a concussion or worse.
My mandatory list of equipment when I taught (1985-1994) was:
2) Boots with a heel (so your foot won't run through the stirrup)
3) Long pants (good fitting jeans were fine for beginners)
5) Gloves (the cheapest were the stretchy ones with pebbling on the inside)
I still use those to groom my horse's faces and apply fly wipe to them bc they are friendly and gentle. I got ALL of my students to buy from (then mail-order, NOW online) horse-supply catalogs. I felt that everything that I asked them to buy was an investment in equipment to use if and when they bought their OWN horse. I also had a "red nail-polish club". I used to wear it to remind them to always wear their own gloves, and it caught on. Please do NOT wear earrings, and especially dangly ones when you ride. The mane is course and you can get it caught in the earring and rip your ear.
When I took Hunt-Seat lessons, we had to buy:
I ride in jeans, now, but after a few more months of successful dieting I'll be asking for full-seat breeches for Christmas! MWA, HA, HA!!!