Well, independent of the exact combinations we have available: ##H \to \tau \tau## has been observed clearly. ##H \to bb## has some notable evidence already, and it will probably follow as soon as CMS gives an update with 2016 data.
Then we will see the Higgs decays in more production modes and more accurate measurements, but no new decay channels until the HL-LHC runs.
The decay to gluons is completely indistinguishable from background. The decay to charm is impossible to see as well - a factor 10 smaller branching fraction and a factor 10 higher background than bottom.
##H\to Z \gamma## will go from upper limits to measured branching fractions after Run 2 (2018), but with an expected significance of something like 1.3 sigma.
Here is an ATLAS study, predicting 2.3 sigma with 300/fb (2023) and 3.9 with 3000/fb (~2035).
##H \to \mu \mu## looks a bit better, with the HL-LHC dataset it is expected that both ATLAS and CMS get a bit over 5 sigma.
There are also more exotic decays to specific hadrons, but they are rare to be found even with the HL-LHC (assuming Standard Model branching fractions).