15 minutes if you have tokens and OSRS GP are insanely lucky. I'd guess you're having a few hours, but probably more. Priest In Peril, Lost Tribe, ANimal Magnetism, Wolf Whistle are all short, and should not take more than an hour each. Ghost's Ahoy along with Fremmenik Trials are a bit longer, but neither are extremely long.
The gear for Slaying and Training should be the same, and depends slightly on what you're fighting. Castle Wars probably doesn't matter as much, but the best atk bonus for any style you decide to choose. The chances are that you'll simply be cannon fodder the 138s in the event that they decide to play. I'm at 115 combat and the best me is reduce the intensity of the players for a couple of seconds.
Soul wars, it doesn't matter much. The range weapon may help maintain activity, but in the busy worlds, it doesn't matter just as long you're hitting the same thing every few minutes. It's going to be the barragers chinners and 138s with 99 slay who will dominate the day. I personally would rather ignore soul wars completely. Barrows, read a guide. Decide on your strategy and then adjust your gear in accordance with what it recommends.
If you're able to acquire a TokkulZo, you should use that instead of an archer's ring: it is a part of the oldest Kiln quest and is +4 on all combat stats with the exception of prayers and power, making it more powerful than the archer's ring. An amulet of ranging is likely to be a better option to purchase over a fury. It is more effective in defending against attacks with a range bonus , even though it protects you in a lesser way and has zero prayer bonuses.
You won't need a robin cap or hood, but you will need an archer helm: for simple stats checks the archer helm has higher defence but the robin hat offers +2 more ranged offense. It's really your call, the differences are small. Robins work well as a cosmetic item . It can be recoloured for buy OSRS gold loyalty points at Xuan in burthorpe or Varrock, although.