For the photos you can't go wrong with Simpleviewer (click here).
Use it in conjunction with Picassa (click here) and it is a very simple straightforward process to create a gallery.
I use it on my website for photos (click here). Simply install Picassa to manage your photos on your computer. Install the SimpleViewer template and then Picassa will automatically create the web pages for you to upload to your webspace. You can edit the template to make the page look the way you want it to.
As for the videos, it should just be the case of uploading the videos to the webspace and then uploading a web page with hyperlinks to the files.
However, a note of caution. If you are putting videos on the site, they take up space and bandwidth. If a lot of people are going to be accessing them, you may run into extra costs from the website host for the amount of traffic the site is generating.