Managed VPS For Large Video Site

I'm currently building a large guitar lesson website that will launch around the end of the year or so. Basically there will be multiple instructors on the site who submit video files from 10mb to 20mb in size each. There will eventually be a couple thousand videos on the site, so around 30gb of disk space right there give or take. So I need plenty of disk space.

I'm on a shared hosting account right now with iPowerweb, and that of course won't do me much good once the site's up and running. Plus they have a 12mb upload limit, but the instructors need to upload videos larger than that. And I'm aware that with a VPS I'd be able to set my own upload file size limit.

Anyway, this server stuff gives me a headache and I feel totally clueless. I've always loved the basic shared account because I don't have to do anything to keep the server in tact. But from what I've read, a VPS or dedicated server would take a lot of work on my part. So for that reason, I'm guessing I would need a managed VPS or managed dedicated server. I don't totally know what "managed" means, but hopefully to where I wouldn't have to do any upkeep. I need to focus my time on a bazillion other things besides the server, so it'd be nice to find a plan where I wouldn't have to worry about server security updates, software updates, and any other server maintenance etc.

I need tons of bandwidth. It's going to be a membership site with hundreds and eventually thousands of members who all watch the lesson videos. So that's a ton of bandwidth. I'll be the only one on my server though, I'm not going to also host clients or anything.

I'll of course need super reliability. With eventually having thousands of members, my site needs to be totally professional with near flawless uptime.

So I'm thinking I'd want to start off with AT LEAST 40gb of disk space, but 60gb might be better. At least 1000gb transfer, but again, maybe more? And I guess a lot of ram, although I admit I hardly know what ram is haha, does that have to do with the speed of the site? And what's burstable ram? But yes, I'd need to have a server that can handle all the many files and users, with great uptime and great speed.

Budget-wise, I'd like to keep it under $70 or $80 a month if possible. If absolutely necessary, maybe a little more.

Anyway, if you guys were in my shoes, what would you do. Assuming you're clueless about VPS, and have the needs mentioned above. Any host recommendations or advice?

Price-wise and size-wise, Start Logic looks pretty good, but I think their VPSs are all unmanaged. Ive looked at a lot of other companies, but it's hard to find the right plan.