Well, I do not know your slayer level, but I can say Slayer is
one of the most profitable and exciting skills to train your
combat. Slayer is a slow skill so I would be uncertain on how long
you are willing to fight monsters. The only way to train Slayer is
by getting Slayer tasks from the Slayer masters so try there first.
Speaking to the Slayer master in the Edgeville Dungeon should be
good for you. If your Slayer level is low then try speaking to the
lower-level Slayer masters first and then build up to better
ones.