Nick,
I am not personally involved in drop-shipping, but have had contact with someone who has done/does this successfully.
The steps he went through:
1. Negotiating with suppliers for special prices.
2. Shipping:
2.1. whether the supplier offers shipping, and if so, at what sales price level could they offer it free.
2.2 when the supplier doesn't offer shipping or is too costly, he also negotiated with courier companies.
3. Negotiate special rates with payment proccessors in your country-since you would obviously want the money at your disposal. Important: find out the timeframes for payment to reach you, especialy payments with credit card-which can be charged back. That said-use a well-known payment processor, as this would be best in such cases.
4. Does the payment proccessor have an API which can be intergrated with well known eCommerce software? For example, Paypal does-but it may be limited to certain countries, e.g. US/ etc, and Paypal is expensive is this regard especially if margins may be low.
5. Finding an eCommerce platform that suits your needs. The best one from own experience, is Prestashop. You customize it to your liking- some php, js, css, html, etc. There's Magento too. These have so many features packed into it that make a NPer go WOW! :D
6. A good host for your site.
Hope that helps.