You definitely want to build a custom solution, and you definitely want to charge a lot more than you normally would because there's a lot of risk and due diligence needed.
As for your architecture, using NoSQL is possible and there are some compelling reasons behind using NoSQL for ecommerce - the main reason being that it is schemaless and if you have a ton of categories and a ton of products which all need to be sold differently (ie you sell computers differently than you sell watches) because the product attributes are different, managing database complexity becomes really important.
This video will show you what a really forward thinking start-up in NYC is doing. They're using MongoDB for their entire product database. This video should be a real eye opener as it outlines a lot of the pitfalls in MySQL for big ecommerce sites, and alot of the game-changing potential of NoSQL:
http://engineering.shopopensky.com/topics/mongodb
As for handling payments, you definitely do NOT want to store those in NoSQL. Keep your users, sessions, and payment data in MySQL and make sure it's highly secured. Here is a great (even though old) piece on securing sessions in PHP applications:
http://www.troubleshooters.com/codecorn/php/persist.htm
As a note, this last link should help you understand the theory better. Most PHP frameworks support this type of session handling out of the box. CodeIgniter, Yii, and ZendFramework are among the best.