I have traditionally used GFYCat for a few things, but their uptime has been questionable lately; on last use, clips that I uploaded stayed in the “Encoding” phase indefinitely, and were discarded when I came back. Searching for “video hosting site” tends to produce ads for many business-focused cases, not necessarily made for embedding into a site like Lemmy.
Depends on the size of the video, in the micro blogging sphere regular videos up to a couple dozen MB can do just fine, even for small/single-user instances (the media store would occupy a few hundred GB). It’s up for the instance to employ a CDN, although usually unnecessary at the current scale. Instances lacking resources can either disallow large media or run garbage collection on old posts.
Alternatively you can self-host the media you post; what I’m trying to avoid here is to hold them hostage in another walled garden, since they’re integral part of a post. It doesn’t matter if they are just memes, if they’re important enough to be posted, viewed and commented on, the context should remain intact, so we should try our best maintaining that instead of relying on big tech.