If you have a video file then you need an image to represent your thumbnail. To create a link that will allow someone to download the video is as simple as:
<a href="url of your video file">
<img src="url of the thumbnail image"/>
</a>
Then the user will see the thumbnail image and when they click on it they will get the video. If you wish to embed the video in a player you can select the player of choice such as FlowPlayer or any of a million others.
You question about you-tube I assume you mean to embed you-tube videos on yout site. If that is the case visit the video on you-tube and there is an embed text box on the page with the code that you must copy and paste into your site.
EDIT:
The FlowPlayer that I linked to (not an endorsement) has a page that describes in great detail how to do what you are asking for here. If you follow each step then you will get exactly what you envision.
Another Edit:
To play a particular file format you need to use an appropriate player. I do not know all the players but you want to make sure that the format you use is popular enough so that users do not have to download special plugins just to see your video.
If you visit the DivX website you will find their embeddable player that can play mkv files on your website. They have a Code Generator that produces the code that you will use to embed the player on your site.
As for various options like starting in pause mode etc you will have to read the documentation of the player that you use to see what options they allow.