You say that you need the bike for urban transport as well as rough trail use.
You can do all this on a hard-tail MTB. Dont ride a high-end bike to school, it will get stolen.
All the big brands (Trek, Giant, Specialized, etc) make good entry-level MTBs ($3-500)with threaded eyelets for fenders and luggage rack. They are OK off road. If you go midrange ($5-800) you will get something lighter and more fun.
There is no need to go higher unless you have lots of money. If you do have cash to burn, get 2 bikes, one fully rigged for everyday commuting and one for fun.
There is no problem with the quality of Taiwanese-made frames.