Here is a link on shock chlorination of private wells. It gives you criteria about when to chlorinate and tells you how much household bleach to add to the well (3 pints per 100 gallons in the well).
I think they go farther than necessary where they tell you to shock chlorinate the well when you open the "distribution system", which is just your household plumbing.
I would shock chlorinate the well per the information at the link if I got a positive test result for coliform bacteria. After you shock chlorinate you should test again to see if it has done the job.
http://www.water-research.net/shockwelldisinfection.htm#SHOCKCHLORINATE
You could put a little household bleach in the well (about 1/2 cup per 100 gallons of water in the well) if you are concerned about contamination from opening or working on the system.
If you get a repeat coliform test after chlorination and still want to use the well, then you can chlorinate and filter. Chlorine will kill the coliform bacteria and viruses, and the filter will remove sediment and larger organisms. The following is a "simplified for home use" adaptation of what I install in small systems that use water from lakes and ponds for public water supplies.
1. Install a chlorinator that will add a small amount of chlorine whenever the pump runs.
2. Put a filter in the system that will remove organisms that are not easily killed by chlorine. Those include
giardia lamblia and cryptosporidium.
If you want to see what crypto can do, Google "milwaukee cryptosporidium" and look at the first few returns. After you read those, try "cryptosporidium seneca lake".
If you decide you want a filter take a look at
http://www.harmsco.com/uploads/pdf/harmsco_polypleat_catalog.pdf
I use the PP-BB-20-1 which is on page 3 of the link above. A generic "Big Blue" housing can be obtained for less than $50 and the Harmsco brand cartridges list for $69 but are sometimes available for less. One cartridge should last a year of normal household use unless you have a very bad well. If your filter plugs up you should not be concerned about the cost of the cartridges; you should be grateful that you are getting that stuff out of your drinking water.
A chlorinator and filter will cost less than $500 for parts including a Hach CN-66F chlorine test kit that you should use if you are using chlorine regularly. It's a pretty easy do-it-yourself installation. If you want more specifics, come back with another post or an Email.