For my business, this is want to happen:
1. My customers come to my website and sign up by entering their
customer ID (which they should already have) and setting a password
and enter their personal information.
2.They can sign in to make purchases. (By entering a product ID and
quantity).
3. They can check the status of the order by signing in. If their
order was shipped, it will have a link to the UPS.com website where
they can track their order.

What would be the best way to do this? I was hoping to use something
free like oscommerce. What would you recommend for doing this? Thank
you very much if you could help.

I've seen something like that at http://lcsdesign.net