I've never ordered from the site, but it lists PayPal as a payment option on the bottom. That is a good sign. PayPal is generally a secure payment option. If I was to order from them, and had no references, I would use PayPal for payment. It works when you are ordering from random people off eBay right?
May I suggest Googling the "website name + reviews" to see if anyone has given a negative view on the site?
Just thought I'd throw in some tips!