We would like to develop a Shopping Cart application on SharePoint 2010, any pointers?
I would highly recommend msdn as a start for ecommerce:
Introducing SharePoint Commerce Services
also look into what they already have for you setup and weather its the right thing for you using webparts:
Commerce Server Web Parts
as someone on msdn has noted:
That being said you have thoes choices:
third party shopping cart at $89
How to build a no code shopping cart with SharePoint 2010 – Part 1: Background
Open source commerce:
also there is another question asked simmilar to this ;)
hope it helps :)
Besides all of these, please read the below Question:
I completely agree to that, SharePoint may not be the proper selection for building such solution, you should go for ASP.NET Application instead!