How to choose Bluetooth headphones?

Question

Headphones

I want to buy my first Bluetooth headphones. I take for a Samsung Galaxy smartphone to walk in them on the street and in transport mainly, although I may also go to the gym with them. I plan to only listen to music, talking on the phone through them is of little interest. So far I've only used wired ones. But I'm tired of endlessly tangled wires that take 5 minutes to unravel. There are several questions to choose from:
Overlays or inserts? This is perhaps the main question with which I can not decide. I tried a lot of wired earbuds and always the same problem - they fly out. Xs, maybe some of my ears are not like that, but it’s very difficult to find such liners to hold firmly. Here are the last ones that I also had at first flew out, but then I changed their ear cushions (pad) to smaller ones (it was included) and finally began to more or less decently hold on. On the other hand, if you take consignment notes, then I’m thinking - how can I walk in them in winter? You can’t slip them under a hat or put them on over ... It turns out that in winter they are generally useless?
The second question is the price segment and the company. Like everyone wants to save money. : D Does it even make sense to take budget options for 2-5k rubles? Or are they so bad that they fall apart in six months? And which firms are better in terms of price / quality ratio?
PS In terms, maybe I'm not very in the subject. By earbuds, I mean anything that goes into the ear and doesn't have a big headband. And under the overhead, respectively, with the headband and over the ear. Moreover, it is desirable that they wrap around the ear, and do not press against it. And then when they cuddle - you listen for a long time and your ears start to hurt from pressure. I had such wired computers.