For every new seller, the starting point is Ebay. However, given the complexity and the competition, you may not like Ebay when it comes to getting the desired price for your work. Although, some make a considerable amount through the site, but this is largely because they are now established brands. Overtaking them will take time, but you can easily have a quick idea of the market demand and the current situation.
Other prominent option if Etsy. It has grown immensely over the course of the past couple of years and focuses on all handmade items including photography, jewelry, and other craft products. Etsy could be your perfect answer for not having your own website, and further assures you good price if the product is in demand.
The major factor that comes into play for such sites is pricing. For prices are generally higher but the buyer understands that the product he will get is top-notch. Furthermore you will have PayPal to process each sale and collect your payments. Amazon could be another online option for you but the payment dealing is a little different from Etsy which probably will discourage you at first. However, all will still depend on your preferences.
With the advent of social networking sites such as Facebook, your task has become easier. However, while using it to sell your item is common, you must make note of other things before you put your work online. The first task is to market your product as you cannot expect to sell it instantly.
Also, with the competition around, you probably need to be efficient by ensuring that your product stands out. You should be able to differentiate your work and then gradually work on who you think will buy it. Also have appealing photographs posted which makes it easier for people to gauge your work. Learn the essentials about target market.
If you are still left unconvinced, try out designing your own website. Hire a professional if needed. Make sure that the website is secure and the customers can navigate it easily.