Raphael Thys
It's generally a better idea not to make registration/sign up mandatory in order to complete a purchase. It's much easier for a user to have registration as an optional step after the purchase.
E.g. a user completes a purchase and has already entered all information (Name, e-mail address etc.). Her intended task, to buy one of your products is then completed and she's ready to be taken somewhere else. Now's the right time to ask him to provide a password for an optional account.
If the user's already registered then it might be a good idea to ask for the credentials before completing the check-out form (avoid letting her fill out a form with information you already know)
The problem of mandatory registration is also addressed in the 300 Million Button article.
They took away the Register button. In its place, they put a Continue button with a simple message: "You do not need to create an account to make purchases on our site. Simply click Continue to proceed to checkout. To make your future purchases even faster, you can create an account during checkout."
The results: The number of customers purchasing went up by 45%. The extra purchases resulted in an extra $15 million the first month. For the first year, the site saw an additional $300,000,000.
Here's another article about basket abandonment that also illustrates my point and offers some more interesting hints.
Clothing retailer ASOS managed to halve its abandonment rate by removing the need for customers to create an account.
However, the sneaky part is that customers actually still create an account, it’s just that ASOS removed any mention of registering.