I was already told that it's extremely urgent that I replace my car's tires. It's 5 years old and a few months now. I knew since last year that the front tires are super worn out already but it's my fault that I'm a procrastinator. What type/size/brand of tires should I be getting? I'm looking for bang-for-the-buck ones (not super expensive).

For the meantime, if I have the current rear tires (thicker) and front tires (thinner) switched, would that at least give me safer driving?