Running doesn't require a lot of equipment, but it's REALLY important not to choose inexpensive over health.
Investing in REALLY GOOD shoes (which are usually expensive) is absolutely important. So is investing in proper care for injuries. It defeats the purpose of exercising/running/getting fit/improving your health if you incur injuries and don't properly health them
Runners have incredibly high rates of injury (something like 40% of runners every year get injured?) so if you look at the total cost of investing in proper shoes and injury cared, running is actually not that cheap.
Sorry for the rant, I get injured often and know what happens when I put off taking care of injuries and wouldn't wish that on you. Best of luck with a speedy and safe recovery