My first lab water test was from
http://e-watertest.com/. $160 seemed very expensive at the time, and KarLabs at $60 with them paying postage both ways was wonderful. With KarLabs gone, I might go back to e-watertest. Their Priority 100 for $99 tests for most things needed for water treatment design. It does not include sulfate, but people don't normally treat for that. They provide a home coliform bacteria test. Their Priority 200 looks good for an initial test that includes some unlikely stuff. My first water test had a bunch of things marked nd (not detected). Prepaid return shipping label is included for US customers.
http://e-watertest.com/order-water-test-kit/
NTL Labs is by far the most recommended here.
http://www.watercheck.com/ Well trusted.
They want you to overnight shipping, so that will drive the price to over $200 for most people. Even with overnight, they don't test for H2S anyway. Overnight may not be fast enough for H2S.
http://envirotestkits.com/product/safe-home-select-drinking-water-test-kit/ $99 looks good.
If you care about the coliform test results, care needs to be taken in
sampling.
http://www.ugra.org/pdfs/SamplingHandout.pdf is one description
of a method to avoid contaminating the sample.