I'd recommend Tubby's setup using the mystic boot and Ring of Life until you're confident, then you can start risking a bit more expensive equipment RS Gold. 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 and 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're not able to find an fruit bat, bunyip is what you need, although that will limit your excursion since it will only heal at a rate of 80LP per minute. If you notice that your journeys are too short when using tortoise/bunyip then you may need to bring Guthans instead of Veracs and supplement your Bunyip's healing by attacking Spinolyps.

If you own the Enhanced Excalibur that you have obtained from Hard Seers Diary, it's recommended to use it because it is able to restore 200LP every five minutes as well as raise defence. Once your tortoise is empty you'll need to detach it and get out the fruit bat.

Make sure you have brews and restores available to heal in an emergency i.e. don't use your fruit bat if you're out of brews in case you accidentally kill Rex then it could get ugly Old School RS Gold. Do not forget to have a one-click to teleport in the event of an emergency.