I am basically exclusively Linux now and my preferred tool set is:
RawTherapee - Raw development, support pixel shift with lots of options. There are lots of options to play with and it has a much steeper learning curve than Lightroom but I find it to be much more capable. I don't know how it handles the incamera HDR stuff but I never use that and instead shoot bracketed shots and process elsewhere.
GIMP - General editing for things I can't do in RawTherapee. I use it for a lot of astro images but for other images not so much. I would recommend getting the resynthesizer plugin for it as it adds a number of features that are similar to the photoshop context aware fill.
Hugin - For creating panoramas, various stacking, HDR (actually enfuse and I like the enfuse look more than regular HDR) and various other things where working with piles of shots becomes useful
Astro Pixel Processor - Used for astro stacking and some of the starting astro image processing like color correction, light pollution removal, and graident correction a special purpose tool
For sharpening there is a lot that can be done using RawTherapee when working with the detail tab with things like the various sharpening methods (unsharp mask and R&L deconvolution), and contrast by level. Going beyond that in the advanced tab there are all sorts of wavelet options that can find lots of detail and bring it out but again this has a steep learning curve and can go sideways really fast until you have some idea of what is going on.
When it comes to noise again RawTherapee has lots of options for dealing with it under the detail tab with lots of little controls. Here again playing with the contrast by levels sliders will make the best use of things to preserve detail while squishing noise. There are also tools under the wavelet section in the advanced tab that can also deal with noise but I haven't mastered those yet.
Another good option for Raw development is Darktable which has much more of a Lightroom feel but again has many more options and tools. It is easier to learn but still a really powerful tool.
Originally posted by ThorSanchez The dev version of RawTherapee apparently has local edits including spot removal,
That would be really nice as that is most of what I do in GIMP with non astro images.
Originally posted by ThorSanchez Some people also use Hugin for HDR but I could never get satisfactory results.
The GUI that sits in front of it kind of sucks and hides a lot of the controls so for stuff like that I use hugin to output remapped aligned images that I then manually stack those using enfuse from the command line.