Not sure if this is the answer you were hoping to get, but here it goes anyway
Getting your own server is likely going to end up giving you more pain then pleasure unless you have resources available (namely money, and people) to deal with a larger scale project.
The reason I say this is because if you have to ask, you’re probably not ready for all the other stuff that you haven’t asked about
I may be completely wrong, but I’ll assume that the reason you’re unhappy with your servers is because they couldn’t provide you with the bandwidth to support video streaming and file hosting (not without increasing the price substantially)
If that is the case, I may offer a simple and elegant solution that won’t break your piggy bank, and will solve your troubles:
Stick with the usual hosting suspects for your website, but place the files and videos on AmazonS3 server and embed them into your site from there. It costs pennies for terabytes of data, it’s fast, and the user won’t even know the file sits on the external server.
This is the service that Amazon itself uses, so in terms of speed and reliability, you’re more likely to win the lottery than experience downtime.
Not to mention that the 7-or-more-figure big shots in online marketing use this service for their megalaunches when they send thousands upon thousands of viewers to watch their sales videos.
That’s the kind of viewership that would likely put a serious dent into your own server reliability
Hope this helps