The main "tool" in Doctor Who is the Doctor's sonic screwdriver. It can literally unlock, lock, fix, and blow up anything (except wood.. he always says "I really need a setting for wood").
9 and 10's sonic screwdriver
11th Doctor's sonic screwdriver
The Doctor doesn't use any weapons but his companions do sometimes. Rose uses a huge freaking bazooka that shoots plasma in the episode "turn left", Martha becomes an agent for UNIT, and Captain Jack Harkness often uses a pistol. His wife, River Song, uses a plasma-esque shooting gun.
Another time travel deice used is a vortex manipulator (worn on the wrist, mainly by time agents)
Sorry for the huge response!