I don't know much about authorize.net, but i've implemented a shopping cart with paypal IPN before.
Basically what happens is you set up the transaction, then redirect to paypal to allow the user to enter billing information etc. When the form is submitted paypal contacts your site using the...
A short term solution until you can upgrade to MSSQL might be to do a compact & restore on the database. That should shave a few megabytes off the database