Quartz watches will generally work, but they will be somewhat disposable in build quality.

Mechanical watches are disposable but they can work well enough if they are working well when you get it.

They aren't the best value unless you get lucky. I'd usually recommend an inexpensive Casio ($10-40) for a good inexpensive watch that will last a long time. Some of them have 10 year batteries and some might be solar charging as well.

BTW any good watches under 300 for me to buy for my birthday

A good Casio watch, a Citizen Eco-Drive model (many different options), maybe a Seiko quartz or Bulova watch. These all would be good watches.

For mechanical watches, Seiko, Citizen, Bulova, and Orient are what I'd look at.