I am an Australian based freelancer with 5 years experience working with Wordpress. I know everything there is to know about Wordpress (the core, writing plugins, new functionality, themes). What you are asking for sounds pretty straightforward to me.
Essentially I would make it so you paste in your Youtube URL(S) in the backend and then on the front-end not only would they display, but I could also get it to fetch the appropriate video thumbnail image from Youtube as well. I would advise against hosting your own videos on your server as bandwidth can be pretty expensive and Youtube is free and easy-to-use.
As for photos and galleries my solution would utilise Wordpress's pre-existing gallery functionality, but of course it would be a whole lot smoother and work nicer on the front-end of the site. I would most likely use the Colorbox plugin for displaying the gallery images. If you would like to see existing examples of where I've done this, I can send you some links in a private message of existing Wordpress sites I've done which have video, photo galleries and whatnot.
While I don't want to put down any of the other bidders, my communication skills are A1, my Wordpress programming skills are extremely high and I pride myself in writing the cleanest possible code. The solution I provide will be guaranteed the easiest solution you'll come across at this price point.