Any kind of welder will do.
A stick welder will do and would be the best technique to learn first, but requires you to cleanup every weld.
A MIG is the easiest as it's almost like holding a metal glue gun, but proper welds require some practice.
A TIG welder is in my opinion the most peaceful technique, but requires the most amount of practice.
If it's for production runs of multiple gym equipment, MIG is the fastest technique.
Get whatever suits your price range and practice, practice