There is no right answer here without knowing more of your circumstances. There are too many "it depends" to just say used or new. Both have pros, cons and unknowns. And those pros and cons also differ between makes and models.

• Do you think you'll sell it within a few years or are you convinced you're going to try to keep the vehicle for as long as possible? (Selling means depreciation will hit you, so you have to figure out what depreciates less, usually used but not always. The cheapest used car you can find will likely be the one to depreciate the least. Long term means you want longevity which will probably be a new vehicle, but not always. A new manual transmission Nissan Versa will likely last much longer than most, if not all used $20,000 vehicles.)
• Is a manufacturer's warranty important to you, or will have some money set aside for any sort of mechanical repairs? (If you lease or trade in every few years a new vehicle can keep you within warranty, which means you don't have to worry that much about mechanical failure. Some used vehicles, like Toyotas, usually have good reliability, but regardless, no warranty means you'll have to pay for any mechanical failures. If you buy used make sure to get a pre-purchase inspection and do your research on which cars are known for reliability).
• Is there a certain brand or type of car you're mainly interested in or have to have? (Do you need a pickup for your type of work, or want an SUV or crossover, or would an econo sedan or hatchback work? Are you a Mazda fan, or do you dream of owning a Tesla? All of these questions may mean you have different needs, wants and priorities than other people, and that's ok. Some people love driving a VW because they're fun, although not the best reliability. But others feel that reliability is most important, like from a Toyota Corolla, in spite of being a more conservative or "boring" vehicle. Some people also want the latest and greatest infotainment tech or safety features. Others couldn't care less if their car has a radio or seat belts.)
• What will your insurance costs be? (There are people who buy cars and then can't afford the insurance. And this can vary, not just between used and new, but from car to car. Usually newer cars have more expensive insurance, but not always. For an example, I was looking at a Tesla Model S that's priced at around $15,000, so some $200 per month for payments, but I was quoted at over $400 per month for insurance on that car. By comparison I was quoted for an old Geo Metro at $30 per month for insurance and on my current 2013 Toyota Avalon I'm paying around $130 per month for insurance. You're numbers will likely be radically different, so call around before buying a car you may not even be able to insure. Some people can't get insurance for Hyundais right now in certain states.)
• How far do you usually drive and what are the costs of gasoline (and/or diesel/or and electricity) in your area? (A used Chevy Bolt may end up being the cheapest to drive with electricity being much cheaper than gasoline in many places. In the world of gasoline cars, many newer cars are getting better fuel mileage than ever before. However, the change from 20mpg to 30mpg isn't as big as 40mpg to 50mpg. Do the math, especially if you have a lot of driving to do on a budget.)
• What do you need/want this car for and how dependable does it need to be? (Again, there are so many things to think about here. You may have alternatives to owning a vehicle, such as public transportation or a bicycle or friends that will pick you up for work. You may looking for a car that will be your only means of transportation. Maybe you want this car for fun weekends. Maybe you want it to commute to work. All this will influence what kind of car might be best.)