Vegan cosmetics and personal products are really easy to find these days, and are often cheaper or the same price as their non-vegan counterparts. My favourite is easily Plant Essentials, a Townsville-based business (who don't pay me!) that makes their own plant-based, cruelty-free products locally, with incentives for re-using jars.
But if you're looking to go off-the-grid with your preening, there are plenty of options for you. The internet has millions of possibilities, but I can only speak from personal experience, so here is what I do.
For my hair, I wash with bicarb soda. I follow that up with a rinse of apple cider vinegar. And I dab some coconut oil onto the ends, to keep it looking fab. Read all about it here.
For my face, I oil cleanse. Instead of soap, I use a combination of olive oil, castor oil, and eucalyptus oil. After a thorough rinse, I moisturise with some jojoba oil. Read about it here. For make up, I use Plant Essentials mineral make up.
For my armpits, I use a combination of coconut oil, bicarb soda, and corn flour. This works really well for me, even after exercising in the tropical summer. Read about it here.
For my skin, I use coconut oil. At night, after a shower, I just rub some in to my arms and legs. Not every night, but when my skin is feeling dry. To exfoliate, I try to body brush, but I often shower after exercise and I don't like body brushing when I'm sweaty, so I use a plain old loofah in the shower.