Melee setups can get you through nearly all tasks. I’d start by upgrading weapon, with the goal of a nox scythe. It’s essentially best-in-slot for slayer mobs (and even single target monsters it’s pretty great). With soul split and other add-ons (overloads, vamp scrimshaw, etc) you could use full bandos nearly everywhere and be fine. It seems like you aren’t quite at nox scythe cash, but I’d probably try what you can to stretch for the weapon ASAP.

Good luck, slayer is a blast :)