I've got to host and serve videos on demand at my job. Any ideas?

So, to briefly summarize my situation: I'm the only tech person employed in a non-tech company in a strictly non-tech business area. Under my guidance we've started to branch our business into web educational content, selling online courses and webinars. It's all been fine and dandy, our experiments have shown that it's worth continuing but now I got to figure out how we're going to host our video content and serve it. Previously we just used private YouTube embeds in our customer-facing LMS, but with the ads on YouTube, the user experience could be better. I'm also not 100% sure it's according to YouTube's TOS. We would've used Vimeo, but their new plans are simply not viable. The monthly video upload limits are too limiting and while we won't hit the 2TB monthly transfer bandwidth now, it'll become an issue in the next months. I've already built ourselves a nifty little website where we can sell and fulfil customer orders an