A torrent that you keep seeded works, since trackerless torrents work well these days. A lot of the free sites have limits of some kind (50GB storage is typical). For paid solutions you could use dropbox (which lets you give public URLs for files). That's a buck a gig a year, with no limit on bandwidth but they'll temporarily limit access if you transfer too much via a public link. There are sites like MEGA (500GB storage with 1TB transfer for 10 euro per month), you could look into those. There are VPS servers with lots of bandwidth that you could look at, but they're more expensive since you're renting a VPS rather than just file hosting.

Maybe somebody knows a decent free solution that can handle 150+ GB of data and lots of transfer? All I can think of for free is BitTorrent.