Cheap car brands that i would personally recommend are:
Honda: Generally accepted as a dependable and cost effective brand Honda has many "Cheap Car" models that are worthy of purchase. A few of these include the Civic and the Accord. With a front-wheel drive configuration and a fuel friendly 4 cylinder engine the Civic makes a wallet friendly choice. Whereas the Accord with an available v6 engine still has a reasonable fuel economy and great owner satisfaction ratings. With Honda engineering the motors produced have been known to reach miles of 250,000 miles and above.
Toyota: Toyota has been a go-to car manufacturer for a number of years with models in their line-up ranging from the economy Corrolla to the family type sporty Camry. A cheap car that is a Toyota may seem to many as a seldom or rare occurrence but through simple searching one could easily find a well-priced toyota to suit their needs.
These two manufacturers are prime examples of quality engineering and reliability. But please don't limit yourself to just a Honda or a Toyota. Be more open when choosing a good car maker and broaden out. Remember that the people who have owned them know more about bugs and issues than the manufacturer so trust them. If there is a problem that may arise they have probably dealt with it.
Used or New?
When looking to find a deal on a "Cheap Car" you may wonder new or used? There are upsides and downsides to both. If you are buying a new car and it hasn't been released for more than a while problems with longevity that haven't been explored yet may arise during ownership causing hassle and frustration. Whereas a used car on the other hand has most likely had the bugs worked out from the problems arising under the previous persons ownership. Though a new car hasn't had the possibility of a prior owner abusing it so you get a "clean slate" to start with. A used car may have been beaten and abused causing engine damage that will not be apparent until later in the cars life. So be cautious and inquire as to who owned the car previously and how they drove it. A good way to know this is by getting a Carfax vehicle history report and looking for possible "red flags" on how the car was treated. Never be afraid to ask questions.