The first things to consider is what degree of photography website best suits your needs. To determine this is necessary to explore what you want from the website. What type of photographer are you? If you are a family or kid photographer that wants to show off their party pics family and pet pictures or even vacation pictures you might like to consider the options available to you.
There are loads of social networks sites that give you an opportunity to host your fun pictures in the cloud. There may be some limitations as to the storage capacity you can enjoy. These will be fine for you perhaps if you don't mind ads on your website. You may also go for premium services as well which will not display ads on your site. Sites like Facebook or if you prefer web blogging Blogger or something comparable will also work well.
An amateur photographer or if simply prefer something better then you may like to pay if you are serious about your artwork. These do not have to cost a lot and may be found with most hosting companies. If you're a pro photographer you may need the best possible web site and the best hosting pack. This doesn't necessarily mean the most expensive. There are various options to select from.
You can host your very own site. You can add a photo library and your images or you might join your own web site for pictures and the photo websites which provide you hosting.
Obviously there's nothing stopping you from doing all 3 if you wish to.
One thing that you can also do is to try out free stock photo websites. These websites allow you to share some of your pictures online whereby taking advantage of a large audience who might be interested in your pictures for their projects or something else. Some of the stock photos platforms also support video downloads but that is a topic for another day. Nonetheless, there are many options available to choose from with a simple online search.