I use Instagram, Twitter, and FurAffinity. Although I use Imgur if I upload anywhere else because image links on those kinds of websites don't always work well. In comparison to FurAffinity and Twitter, it's a lot easier to get likes on Instagram. (Instagram does have a lot of bot accounts, though.)

While Twitter does compress images, it also has retweeting, scheduled tweets (using Tweetdeck) and analytics, so I don't think it's all bad.

FurAffinity doesn't really have many good features on there, so it's not that good unless you really wanna do a lot of furry art.

Imgur most of the time. I mainly use DeviantArt/Tumblr for posting personal art or fanart.

Going to recommend deviantArt. dA keeps the quality, is free, has no limits that I know of.

FurAffinity is good depending on how high the, er, rating of your work is. They thrive as a NSFW community in many cases so do bear that in mind, BUT they make up for it with harsh theft rules. They've had some issues with accounts being lost (I lost mine to the bug) in the last few years, but overall, a fantastic choice.

On the other hand...

Imgur has had issues with image loss in recent years, by the site pruning old files out. Not ideal long-term at this point. Overall, still one of the safest bets, but not exactly ideal.

Tinypic got in trouble with some games a few years ago for replacing images with NSFW content since they have absolutely no content filters. Just bear that in mind when using it. Also, they have more ads than a web page made in 2005. I personally don't recommend using them because I had content affected by this issue some years back and lost a few accounts on PG-rated sites.

Photobucket (we all know what site you meant, I'm assuming) is really trashy now and honestly isn't the place it was a decade ago. Such a shame.... used to use it all the time, now I don't bother to use it at all.

Speaking of Twitter, the date that they stop supporting transparent images (Feb 11) is quickly approaching. So... yeah <_<;;

Also: wanted to post this here just in case anyone would find this info to be useful. multiupload.us/ allows you to upload to multiple sites at once (Weasyl, Tumblr, Twitter, FurAffinity, ect.). Saves me a lot of time when I wanna post something. The beta version also allows you to upload to DeviantArt, but since it is beta, expect it to be a tad buggy.

It also supports description templates! I use it to put links to my social media in the description of each post.

It can be tough to keep up with the ever-changing landscape of the internet, and it's definitely frustrating when a service you've been using for a while suddenly becomes unusable.