First to select processes you should perform analyzes to know how much barium, lead and hydrogen sulphide you have in your raw water.
With only air stripping you won't get removal of lead and barium. The treatment option for hydrogen sulphide will be dependant of the concentration of water and pH. Strpping option is limited in efficiency. You may have to look at another process depending on the concentration in your raw water.
Barium can be treated with reverse osmosis, ion exchange, filtering, lime softening and maybe few other processes.
Lead can be treated with reverse osmosis, carbon filtration, distillation.
It should be evaluated all together with the known concentration of lead, hydrogen sulphide and barium constituant in addition with a complete analysis to check what type of treatment can do the job.
From what I know, there's no cheap solution to treat all of those.