In order for you to occupy the house there should be at least a test for bacteria and nitrates and that's for potability. These tests should be repeated on an annual basis (at least) to make sure the water is safe and is staying safe. One of the negatives of living on a well.

Then you're looking at tests for hardness, iron, manganese, arsenic, PH, TDS, copper, sodium, and a number of other things before you decide if the water needs to be treated and for what and then how.

With visible dirt in the water you'll want to give the well a little time ESPECIALLY if you shocked the well. Shocking wells can sometimes treat the symptom and does not cure the disease. Bacteria can return after a while necessitating treatment for that and that treatment can be incorporated with other treatment for other things.

Check around with your local environmental heath department for a recommendation on local labs.

Samples for mail away labs need to be collected VERY carefully and some samples for specific tests don't travel well and may not provide accurate results.

If you can get comparable prices locally that's best especially since a local certified lab will be familiar with water conditions in the local area they serve.

and I'd add that it isn't just time that stabilizes your well. It needs to be "developed" adequately to pull the finer materials through the coarser materials right around the well and through the screen. If you have a lot of fines, some keep sneaking through, and have to settle out in a preliminary tank. But as new as your well is, I'd say it might need more pumping just to develop it.

You don't want to take your water samples until the fines have been flushed out. Your county health department will tell you what samples you need to collect and there are surely some local labs that are set up for the required analysis. Make sure their detection limits are what the county is asking for, too.

Labs at a distance should be fine except for the bacteriological analysis, which has a short holding time. You don't have to have all the tests done at the same lab, though-- you'll end up with different bottles for different suites of tests anyway. Usually you get a batch of metals for one price, I've never heard of paying for each one separately.

Wear clean latex or nitrile gloves and be careful about how you handle the caps where they'll touch the sample. It's not rocket science, just hygiene to keep from contaminating the sample. At 200 feet, I wouldn't think you'd have bacteria unless you're downgradient from a giant stockyard or something...