Hi @Beatrice, portable veggie growing is easy. Some of my veggies grow in big pot, some in milk containers, some in raised beds, some in tubs. All you need is to make sure that the containers you use have drainage holes in them, good quality soil, water and fertiliser, and of course a bit of TLC. All my strawberries are grown in tubs purchased to hold drinks in, they are great as strawberries as the do not need deep soil. I grow all my potatoes in large pots as well. Although I have permanent beds, most gardeners will have some form of portable containers. Good luck with yours.
Welcome to the Workshop community. It's fantastic to have you join us.
Being in a rental is certainly no impediment to growing your own veggies. @Grub80 has given some great advice and I would also direct you to all the raised garden beds available at Bunnings. Of course, you could also build your own. Just let us know if you need a hand with anything - we're here to help.