@Ryan Billingsley
If the carpet is stained and can't be cleaned, you should replace it. The test is, would you live in it the way it is? If not, would your tenant be excited to?
The answer to your question is it depends. It depends how determined you are to find a good deal and to use contractors that provide good value. As always, get at least 3 estimates and try to work directly with those doing the work, not a company with high overhead.
Generally, new carpet in a 4br costs me about $7-800 for upstairs only. You can save money if the pad you have is still usable (if so, tell them no pad). Depending on where vinyl flooring is, if it looks bad, I might replace it with tile. If it looks okay, keep it.
Keep in mind you're running a business. Your product must provide greater value than competing rentals if it's going to attract the best tenants. Find a way to do that without spending too much. A few things that are always worth it: (1) full house cleaning (it should be spotless), (2) decent low-maintenance landscaping (you need to attract prospective tenants into the door (plant some flowers), once they're in, don't dissapoint them/keep them excited...(3) clean paint, (4) nice updated lighting, particularly in kitchen and bath.