Mint will run on almost any PC from the last decade. It requires only any x86 processor and 512MB of RAM, although 1GB is recommended. You'll also need 9GB of disk space, though 20GB is recommended, any graphics card capable of 800x600 resolution, an Internet connection, and a DVD drive or USB port. That's it.
To try it for yourself, just do the following steps. First, if you're converting a PC using Windows 7 or older to Mint, upgrading is quite simple. If you're using a Windows system with Windows 7 or higher, it will come equipped with Secure Boot. While there are ways to install Mint on a system with Secure Boot, by far the easiest thing to do is simply turn it off from your PC's UEFI controls.
Next, you'll need to download the appropriate 32- or 64-bit disc Mint ISO for your PC. If you're not sure whether your PC is 32- or 64-bit, just get the 32-bit version. It works with both Intel/AMD architectures.
Next, you'll need a program to burn ISO images to a CD/DVD disc. Many programs can do this, but I recommend freeware programs ImgBurn and PowerISO. To use PowerISO for installing Linux, you'll need to register it for $29.95.
If your PC can boot from a USB drive, you should get a program that will let you run and install Linux from a USB drive. My particular favorite for this job is Yumi for Windows. Other worthwhile choices are LinuxLive USB Creator and UNetbootin. All of these programs are free.
Given a choice between a DVD disc and a USB stick, I'd go with the USB option. Mint, and any other operating system, will install and run much faster from it.