I didn't start riding until in my 30s, I just do 1 lesson a week. A good instructor listens to what your goals are - mine is just to spend time with a horse, have a bit ride, and feel like I am making some progress in skills. It's very much a 'me in the moment' time, as the horse knows when you're away with the fairies thinking about work and picks that time to be a complete fanny! I've been doing it for 17 years, I'm still not a great rider, but love the experience (90% of the time). The yard where I ride have asked if I'd like to loan a horse, but there was no pressure when I said no.
Pre COVID a riding school would normally be able to rent you a hat and boots, but at the minute I think it's against the guidance. Certainly where I ride they are not renting equipment.
For your first lessons, anything without too much of a inside raised seam will be fine instead of proper jodhpurs (but not slippery, shiny running leggings - the one day I wore them it was like someone had buttered my arse!). Chelsea boots sound perfect to get you started. Trainers are no good because the sole is too flexible, hiking boots are too tread-y. Gloves are mandatory at my school, they don't have to be 'proper' riding gloves for your first lesson, but you have to be able to move your fingers and stuff (no ski gloves!) . Proper riding gloves do have reinforcement where the reins normally run, and sometimes grippy bits to help.
Decathlon is a good place for picking up riding gear year round, and if you check Aldi they might have some of the jodhpurs from a recent special buy available.