Get dark brotherhood, thieves guild and jewelry skill lines unlocked, not sure about the jewelry, but dark brotherhood and thieves guild stay after the free trial 100%
Unlocking the skill lines wont do you any good once you lose access to the zones and cant do the content that levels them up.
True for jewelry. Not exactly true for DB and TG... you won't be able to go to the locations on the map and work on those quest chains, but you can still use the abilities from the skill line.
Also, most importantly, for all three lines, the next time ESO+ rolls around in a few months, your progress will be right where you left it, it's not like you have to start over completely from scratch, so yes, obviously it is worth it to get a head start on advancing those skills.
You can unlock the Blade of Woe, Thieves troves, and if willing to do some running around, Psijic Portals. Will all these be usable without dlc when the trial ends? (I have the dlc/chapter myself so not 100% sure.)