Cross body bags and purses can be any shape, color, design, and style. They can be small clasp purses with a long strap or a tote like bag. I have a cross body bag from Forever21 that is rectangular and holds it shape and I love it's simple design; I can find anything in it super fast.
Cross body purses are great because you'll never lose them or get them stolen, "easily". Invest in one that you love because you'll use it tons!