I believe there are pros and cons for both. Imgur is great because you truly don't have to think about disk space or bandwidth. Imgur is not great because they can delete your posts at any time without warning and leave holes on the interenet, especially if we're talking 5, 10 , 20 years from now.
Should I invest in a beefy server to store all of my photo needs without storage anixety? Or should I just rely on a larger company to handle it for me? I think I'm already answering my own question by writing this post out, but I'd love to hear from the self hosting community.
Both. Use imgur or whatever service you like to actually share so you don't have to worry about bandwidth and hosting. Just also keep a local copy of everything, doesn't need to be a beefy server. Just don't let a 3rd party online service be the only copy.
I do both, at least in the context of linking say screenshots to others.
If I'm linking a very "casual" or non important screenshot then I'll just toss it up on my server and link that copy.
If it were somewhat important, then I'll upload it to my server and imgur and link the imgur copy, just in case my server goes down - doesn't stop imgur from deleting it either but if I get hit by a train and am made unavailable then imgur is probably the best bet.
If it is critically important then I try to avoid screenshots / pictures all together and just describe it in text because that has the best chance of persisting. And if the text disappears, then at that point the image is probably not as useful either.