If you're a member of the Burstinglobs chat room There's always someone who's hybridding and RuneScape Gold needs a mage who is a solo companion to kill Rex for them while they take out Supreme or Prime. That means that you do not need to worry about Supreme or Prime when you're on the road, unless either of you are incredibly bad at what you're doing.
I'd suggest taking Tubby's setup along with Mystic Boots and the Ring of Life until you're certain, and then take a risk and invest in more expensive equipment. If there is no one in Burstinglobs looking for a solo mage, just ask if anyone is hybridding/tribridding and can let you hop worlds from theirs, easier than having to kill Supreme/Prime to start your trip.
Bring a tortoise. Make sure you have a brew/restore ratio that is 3:1. If you can, bring 2 fruit bat pouches and scrolls for when your tortoise dies, fruit fall is only good for soloing Rex, it's not really efficient if you're hybridding/tribridding.
If you are unable to access the fruit bat, bunyip is the only option, although it may limit your travel time since it can only treat 80LP/minute. If your trips are too long with an animal or a rabbit, you might need to bring Guthans instead of Veracs to boost the healing power of your bunyip by attacking Spinolyps.
If you own the Enhanced Excalibur that you have obtained from Buy RS 3 Gold Hard Seers Diary, it's also good to use there as the attack's special ability could be able to restore 200LP every five minutes. Additionally, it raises defence. After your tortoise's tummy is empty, you'll want to dispose of it, then get out the fruit bat.