1. Are you saying that your web hosts terms of service don't allow you to offer ecommerce services or is it an issue with the credit card companies?
2. How is the exchange of money supposed to work? Are you geting brokerage fee's? Is the financial transacrion something the two parties have to work out and you just provide the mechanism for them to meet?

Virtually any paid host will allow financial transactions. You can get a host that supports ms access for around $5/month - mssql might be a couple of bucks more - about the cost of a Big Mac, Fries, and a Coke.

http://www.webhostingtalk.com - www.webhostingtalk.com is a good place to get a feel for hosts. You'll need to understand how you want to deal with financial transactions as that may affect your criteria for a web host.

You'll need to:

1. Find and sign-up with a web host that meets your criteria.
   
2. Register a domain name at godaddy/registerfly/whoever you want and using their services, point it to whatever nameservers your host tells you to use.
   
3. Copy your current site to the new one and tweak it for differences between the two hosts. Typically the tweaks will be things like data base location, email components used, special forms that your old host supplied, etc.
   
   If you're using ms sql db, you'll have to create a new mssql db at the new host and import data to it. You're new host will be able to tell you what you need to do.
   For an access db, you just copy the .mdb file with the rest of the files. Check the WWF docs for how to set it up.
   
4. Somewhere along this process, you'll have to lock your old forum and put notices all over the site directing people to your new url. You can use meta tags on the pages to automatically redirect people if it's ok with your old host.

EDIT: Expect to pay more for cc processing capabilities. Also, some cc processors charge more for intangible items. Trips might fall into that category.