It's different thing of website and hosting even if it depends on each other. First, you need a website that allow registered users or guests to post the contents; therefore, you need website that is dynamic based. For instance, WordPress or Joomla, which are using PHP as scripting language and MySql as Database.

For hosting, I recommend to use paid hosting because it's more robust and reliable than free hosting, but some free hostings could also handle these tasks in the minor condition.

If your web content (uploaded by users) is videos it is best to go for vps or dedicated server hosting.

You need to buy web hosting, it's more reliable to go and pay the cheapest plan for a year subscription.

A good web hosting company will have a script to install wordpress or joomla automatically you don't have to bother on learning about databases and installations.

Once you get for example wordpress installed, you can learn how to get your users post content, etc...

LOL... don't waste your time until you have a complete scope of what you want. There is a Major difference in uploading a text document compared to a video. You need to hire someone or partner up with someone that knows the ropes and not try and do it all yourself. Or else you are going to spend a "fortune" in time.

Yes a database, there is always a database when dealing with customers, clients, visitors... even if it belongs to someone else.
But I highly suggest JVing with a tech...