I’m looking at Dark Templar or Bear Shaman. I plan on soloing as much content as possible
Dark Templar is okay for soloing. Not great, but okay. With the Void of Madness AA trait and good gear they become great, but it is a long road to get there.
Bear Shaman is good for solo play. Sturdy, decent damage output, and self-heals.
Conqueror is also good for solo play.
Avoid Assassin and Herald of Xotli for soloplay, unless you like a challenge. They are fun classes, but fragile. The proverbial glass-cannons.
Most important, however, is to play a class you find fun. All the classes are viable for both solo and group play, even if they can play very differently.
Whats your definition of solo play? I guess 80% of all level 80s in the game was leveled solo. You wont have any issue playing any class in this game solo. The content is either group or solo balanced. You wont really do the group content solo anyway. Pick based on what concept seems cool to you 
Solo play to me is being able to solo open world content that usually need groups. Or possibly instances.
In that case dark templar is definitely the best class. If not maybe the only class that could solo any type of dungeon without obnoxious amount of kiting
DT will perform best for that for sure.
Bear and conq can do pretty similar things but far slower.
Pre-80 though brute conq beats all in most circumstances: the fire banner destroys everything and you just spam knockbacks over and over. Do NOT use the firer banner once you are lvl 80 though, there are far better uses of your cooldowns at that point and the dmg falls off a cliff.
Definitely not Assassin, that’s been my main since 2008. You can do most of the open world stuff by only pulling 1-3 mobs at a time, and all of Khitai you can do most of the solo content but it can be challenging without purple gear if you’re thinking end game level 80 content. Also Herald of Xotli and Ranger imo are not great solo either.