I would recommend you test your wine when it is ready to be bottled.
With that said, I would recommend a "standard profile" that many labs do. It tests for Alcohol by volume, free SO2, PH, acid profile and a couple of other things.
Most wine testing labs I know of are in California. Here are three that I know do testing for home winemakers:
-Lodi Wine Laboratories
-Scott Laboratories (same people that make the ingredients, etc.)
This final test will run you anywhere from $80- $140. I have used Lodi Wine Labs and was very happy with their responsiveness and professionalism.