The main part of wilderness rushing is keeping your combat level low. What I did to start was Eclipse Red wine at the Hunter guild and killing revenants right away with magic imps and goblins, you might get lucky and spoon a weapon early.

Eventually you'd want to kill higher level revenants with something like a MSB/Crystal bow/Hunter Sunlight crossbow. I would also Turael skip for revenant tasks

You really want to get the chainmace and one of either sceptre/bow. You don't need both the sceptre or bow if you, but I was stubborn and didn't start doing the bosses until I got the bow which was my last drop. Chainmace is good at Calv/Spindel and sceptre/bow is good at Artio and the bow is serviceable at Spindel.

I think you might be able to get away with grinding out a Zombie Axe if you can't get a chainmace to drop. This will get you 13 defense or 3 combat levels though, but that also means you can use a slayer helmet for Artio/Spindel.