Generally i'd suggest Don't Starve Together over Don't Starve if you decide to pick it.
Don't Starve Together is more polished than Don't Starve and has quite few improvements and changes towards game mechanics.

Don't Starve (the single player) is only worth it for Shipwrecked and Hamlet but DST has mods that do a pretty good job at porting content from these DLCs

As for staking your place in the world well that's Don't Starve Together in a nutshell aswell :P