For portfolios, you'll need a domain name and a host. If you don't have one already, I recommend
HostMonster or
BlueHost. Both of these companies are fairly cheap and have pretty excellent customer service, and when you make an account for hosting, you'll get a domain name for free. Its not free, but if you want a job you'll have to spend some money. It takes money to make money, as they say. And this is about as close to a legitimate business expense as you're going to get. I personally pay yearly, and write it into my budget so I know I have enough money when January comes around.
Domain names need not be fancy, "yourname.com" is good enough if you can get it, as it'll promote you as a brand and will likely be easier to remember than something you make up.
As for solutions for making an actual portfolio, if you're patient, you can grab
Wordpress for free, and set that up. It takes a while to get used to but its extremely versatile. If you don't know coding, its a good way to learn, but if you're not interested, then it might not be the best solution for you. It has an extremely active community, so even if you're not up to making something from scratch, I'm sure you can find a theme you like and "make it yours."
The other option is
Indexhibit. Personally, I've never used it (I know how to code, so I have no need to), but I know a lot of creatives in my field use it.
The free option that doesn't require a domain name or hosting is
Behance. You'll lose the prospect of "personalizing" it, but it is free, and there's a thriving community. It's mostly used by designers though, as far as I know, so take that into account.
Another important thing to note is with all these solutions, you're still going to need a video hosting service, since it's unrealistic to host your videos yourself bandwidth-wise. On the off-chance you get popular, it will quickly become too much for your hosting plan to handle and a large expense in fees, and it doesn't have to be. For professional purposes, I recommend
Vimeo, if not only because that's what its for. There's no bloat and crap from people just looking to upload silly things, and it's probably going to look a lot better than Youtube in terms of video quality and your professionalism.
Anyway, that's all I got. Hope it helps.
Jam it back in, in the dark.