Running tops - you'll need a selection for different times of year and the weather. As it's coming into autumn, yes, you'll needa long sleeved too, because arms can gat chilled by wind. But if you're always hot when you run, then get short selected and a pair of gloves (sounds slightly bats, but cold hands can be miserable). A showerproof zip up that squashed down to nothing is useful, as is a visor/baseball cap (to keep everything, including the front of a hood if you have it up, out of your face.
Not all socks are twin skin BTW and I don't get on with Kalenji ordinary ones (Kalenji is one of the Decathlon own brands). I think you'll be OK with general sports socks until you're sure you're going to be running regularly. At which point, make your first Wiggle order (they have all the main brands, usually cheaper than on the high street, and you get a packet on mini-Haribo included in every order).
You'll probably need to replace the trainers idc, but starting off in a general purpose pair is fine. But if you are getting lots of aches in your feet/legs/hips/back, then get new ones as soon as you can. It is worth going to a proper running shop if you have one nearby, so they can check if you need a neutral sole or a supportive one, and they can also advise on things like amount of cushioning.
Also think about getting some sort of waist belt, so you can stuff phone, keys etc somewhere convenient,
And also as it's autumn, think about where you'll be running and whether you need to get something bright so you can be seen - if you got a neon/fluorescent vest top, you could throw it on over a long sleeved one for winter visibility, and wear it in its own in the summer.
And yes, 3 lengths of those running tights. Capri length year round, mid-thigh length sold in the warmer months, and full length in the cooler ones.