Let me recap for understanding;

First Ubercart is an e-commerce add-on to Drupal, so references to some of your requests will be addressed first from the Drupal admin then from the Ubercart added functionality.

Control site access to not allow automatic registration? This is handled in Drupal. Administer>User management>User settings

This should work based on your requirement that only registered members can purchase.

Referal verification during registration can be accomplished with rules and actions from workflow-ng.module and/or cck.module assuming the referrer is an existing member.

Membership levels such as VIP can be setup using roles and access control modules in Drupal. http://drupal.org/node/200631

Yes shipping option can be configured for customer selection (mail/delivery/pickup) and calculate associated cost or credit.

Product flexibility exists. for example: Item-shirt, select color(white/red/blue/orange), select size (small $5/medium $7/LG $10/XL $12)
Other product options example for business card where customer choses image or uploads image, fills form with text to print. this too can be done, however it will take research and configureation testing to setup.

http://www.ubercart.org/docs/user

Hope this helps.