I import from card using my own C program that reads the EXIF timestamps and sorts them into directories using the timestamps for directory and filenames (e.g. "yyyy/yyyy-mm-dd/hhmmss.jpg").
Then I would typically use darktable if I want to postprocess. I shoot 99% JPEG. I'll use GIMP for quick edits.
If I want to share, I create an album in Lychee, which is a self-hosted PHP gallery on my web server.
I've never used Photoshop or LightRoom. I have no idea what they're like.
Darktable is great for "dark room" type things. I would put it into the category of non-destructive editing - yeah, you can crush shadows or whatever but the image is still pretty true to what the camera saw. Photoshop enables a lot more reality alteration. Remove/extend/edit backwards, touch up skin, change the color of clothing/objects, etc. I'm not a Linux user, and also am not aware of a great full featured alternative. For quick and dirty on windows, paint.net but that doesn't help anyone on Linux :(
I would definitely be using Darktable for the same purposes as Lightroom. GIMP is more similar to Photoshop. The next version of GIMP is releasing soon with non-destructive editing. I'm looking forward to that.
I've dabbed in GIMP, granted on windows, and I didn't really like the workflow. I guess if you started off in GIMP you might say the same about Photoshop. Here's hoping ABODE gets off the ground. It's not free, or even launched, but it promises a back to basics approach to pricing.
People tend to be most productive with tools they're familiar with, regardless of which tool is actually "better". I figure avoiding proprietary software from the outset was a good long-term investment.