Cats are Carnivores, they are not vegetarian. If you are a vegetarian , you have chosen a lifestyle, this lifestyle should not be forced on your cat! Cats need animal proteins and fats in their food.
I suspect, but cannot prove, that the cheaper the food the lower the quality. Your cat deserves food of as good a quality as the food you yourself would eat.
Good quality branded foods are usually adequate. There are many cat food maufacturers who offer food for cats with various illnesses and conditions. You should work out what your cat will eat as soon as possible after you get him, and ideally you should have been told about his feeding habits when you received the cat. You should select cat food that is described as "100% a complete cat food" . Most cats love Tuna but this should be given as an occasional treat and not as his only food which can cause problems for the cat. Your cat may enjoy raw meat or fish but you should take note that your cat may suffer from worms etc by eating it. Unlike the Tom and Jerry cartoons it's a fact that your cat is far more likely to eat a nice piece of cheese than your household mouse is.
Dry cat food is also very palatable these days and many cats eat nothing else, WATER must be available.
Be aware, some cats are similar to dogs in the speed that they sometimes eat at. Often because of this they eat too much and inevitably it comes back up, unfortunatley the owner won't always know that this happened until they smell it or step in it.
My cats all love single cream, they gobble it up at an horrendous pace, so much so that I now restrict how much they can have in one 'sitting', simply so that they don't bring it back up. I've never met a cat that didn't like cream.
New owners are often horrified to see that cat food has ASH in it. Cat food is prepared at high temperatures and a remnant of ash is unavoidable, you should not worry about ash except that you should perhaps choose a food with a low amount rather than a high one.