I'm a vegetarian and a man and a straight razor user, so maybe I have some special insight into this issue.
I strongly recommend using a straight razor, with quality shaving soap or good cream. Most cheap disposable razors, especially the ones with eight blades or whatever number they're up to, make my face hurt and give me razor burn. This only makes sense: the first cheap blade tugs the hair out, the second cheap blade cuts it, and the whisker slides back down below the skin to get irritated. I have never gotten razor burn using a straight razor.
Plus, it's cheaper. Blades are so cheap as to be practically free, if you buy in bulk from Amazon or somewhere like that. The initial investment in the razor and brush is a little pricey, but if you shave often, it will pay for itself in less than a year. Also, the fanciest shaving soaps are cheaper than canned cream.