Yeah a Fury works, and receiving a Slayer Helmet isn't any issue. In terms of the Ring, I'm not sure how long that takes. Also great job on RuneScape gold winning in Wars, and be certain that you stop while your ahead or you'll lose it all. You could do with swapping your platebody to get a fighter torso, unless you discover you actually need the extra defence (that you probably don't), and I think torag's platelegs provide the best defensive stats as far as barrow's platelegs go. Otherwise, your installation is fantastic for slaying. The only updates you can really make would be - Skillcape or Soul Wars Cape, and a Chaotic Rapier. Also, if you are going to buy Fury / Bandos I would recommend obtaining the Fury first because it's the cheapest but additionally it provides better bonuses than bandos tassets. Good luck.
I'd honestly say there's nobody rewarding skill to train. They all are helpful to some extent, and just training one will not assist you in the long term. That said, below are some suggestions and the reasons behind them: Structure. One you can have a portal room, a menagerie, and a prayer altar, this becomes extremely useful. The portal is actually useful, especially so when you are beginning as a part and nearly all of the teleports you will use are not there. The POH is also great for storage, saving virtually every tool, most novels, and a lot of armour and other clothing.
Agility is also quite helpful: accessing it to 21 is essential so you can use the Varrock-Edgeville shortcut, and obtaining it higher is very beneficial in outrunning critters, huge pursuit places, and even PKers (true encounter there). Getting it to at least 21 should be one of the first things that you do.
Summoning is an excellent skill, but you can't do it instantly. In case you haven't already, unlock 43 prayer with penguin points along with also the troll invasion DnD, and then put them into summoning. Being able to get a spirit terrorbird (level 52) is very rewarding and helpful. What I'm saying is. . .always pick up your charms. It is never worth leaving them on buy OSRS gold the floor.