Um... I'm a welder. Hi :)
if you want clean welds that don't leak, going slow and careful is definitely the best way. TIG or oxy/acetylene would be the best methods becuse they give the most control. If you have never touched a welder, I would suggest finding someone who has and offering many beers. You may end up with a better tank than you had at the outset :)
Failing that, I could fix it for you if you don't mind shipping to Canada.