the chlorine may (or may not) cause a slight 'plasticy' taste to your beer. So, if you get that flavor, don't blame your plastic buckets. If you don't get that flavor - hurrah!
In either case, good job sanitizing! very important, glad you're on top of it!
StarSan can be mixed in small quantities, put into a spray bottle and you can 'spritz' your buckets, etc...very economical.