Otherwise, your setup is perfect for killing. The only upgrades you can actually make are Skillcape and Soul Wars Cape, and the Chaotic Rapier. Additionally, if planning to RuneScape Gold buy Fury / Bandos I'd recommend purchasing the Fury first, as it's the cheapest but also it provides better bonuses over bandos Tassets. Best of luck.
I'd like to say there's only one skill you can train to be a good one. All of them are useful in a certain degree, but only training one won't help you in the long-term. That being said there are a few suggestions and their reasons:
Construction. In the event that you are able to have an area for portals, a menagerie, as well as a prayer altar, this can be extremely helpful. The portal room is extremely helpful, especially when you're beginning your journey as an active member. Most of the teleports you'll be using are there. The POH can also be used for storage, it holds almost every tool, all books, and tons of armour and other clothing.
Agility is also extremely beneficial when it reaches 21. It is vital so that you can utilize the Varrock-Edgeville shortcut. Also, getting it higher will be helpful in getting through huge quest zones, or even PKers (true experiences there). Making it at least 21 should be one of those first tasks you try to do.
Summoning is a great capability, but you're not able to perform it instantly. If you're not yet done so, get 43 prayer by using penguin points, and the Troll Invasion DnD before putting them to summoning. Being able to OSRS Accounts get a spirit terrorbird (level 52) is extremely rewarding and extremely useful. What I'm trying to say is always be sure to take your charms. It's not worth letting them on the ground.