Most internet service providers make free web space available and as this doesn't cost you anything extra, you might as well use this to display your images. Just tell your friends or relatives the address of the web site and they can view your images whenever they want.
If you want a more advanced web site, you will have to use a web hosting service which will provide more facilities like email address, auto responders, site counters and web statistics. There are many available but the one that I use is streamline.net (which is the one I have used for this site) if you are interested.
The jpeg file format is most commonly used for uploading image files to the internet which preserves the image quality quite well combined with a reasonably small file size. However, if you want to upload a lot of files it is worth using a programme like Photoshop Elements or Paint Shop Pro to optimise images to a much smaller file size which means that downloading time are quicker. Another advantage is that you can also have more images on your site that you otherwise could.