Tote bags are a must. I personally carry one with me always as heavy hand bags are not my thing. You can make one for yourself from an old tank top or t-shirt with a pair of scissors and just one seam in 5 minutes. Topshop made a tutorial about it (below), but check also these tutorials by Salt Tree, CraftyNest and Needle&Nest. 

Photos: Topshop, Needle & Nest, Salt Tree.