15 minutes if you already have tokens and rs3 gold feel lucky maybe. I'd suggest you're expecting to take around a couple hours, probably longer. Priest In Peril, Lost Tribe, ANimal Magnetism, Wolf Whistle are all short, and should not take more than an hour or two each. Ghost's ahoy along with Fremmenik Trials are a bit longer, but neither are particularly long.
The gear for Slaying and Training should be the same, and will vary depending on the type of fight you're fighting. Castle Wars probably doesn't matter much, best atk bonus for any style you decide to choose. Chances are though you'll still in the same position as cannon fodder the 138s, if they choose to play. I'm at 115 combat and the best option is to potentially reduce the intensity of the players for a short period of time.
Soul wars aren't a factor to you. A range weapon might help keep activity up but if you're on one of the packed worlds, it doesn't matter what you do just as long you're hitting an item every few minutes. The barragers, the chinners, and the 138s with 99 slay that will rule the day. Personally, I would prefer to ignore soul wars for the sake of it. Barrows, read a guide. Determine your preferred method, and then adjust your gear according to what it suggests.
If you are able to get a TokkulZo instead of an archer's ring: It comes from the older Kiln quest, and it has +4 in all combat stats , excluding prayer and strength making it more powerful than your archer's jewelry.
An amulet of ranging is probably a better thing to buy over a fury. It is more effective in defending against attacks with a range benefit, though it protects somewhat less well and buy fire cape osrs has the prayer reward removed.