Mournhold guards will point you to the sewers to find the Dark Brotherhood, and you find a note signed by "H" on the leader's body.In fact, I'm not sure, but I think you're advised to do Almalexia's bidding in order to uncover leads on the assassinations. My memories extremely foggy though, since I last played Tribunal 7 or so years ago, so it could be that I'm totally wrong. DraQ probably knows...
The main problem I had with Tribunal was the level scaled goblins of doom. I didn't abuse game mechanics, so I fought them legit. While I always came out on top, fighting them took quite a long time, and I had to fight them lots since they respawned in key areas. I remember a single group of them could take out a huge chunk of my weapon and armour conditions.
Otherwise Mournhold was a pretty cool little town, and asides from the respawning Goblins the sewers/caves were fun to explore as well.
After that, you can either try and win Helseth's trust or go work for the Temple immediately.