Buying used Mac mini to run latest Xcode
When I open only Chrome and XCode with a small project, my Mac uses 3.2GB of memory. You don't want swapping. If you only want to do simple programming, 4G of memory will work fine. You will want to be able to open Stack Exchange in the background...
The standard SSD and CPUs will do
Make sure your system is compatible with the latest OSX. If it is not, you cannot test compatibility with the latest version and might not be able to upload your software to App Stores. I would buy a version that I expect to be supported in the next OSX software update.
(currently Mac mini 2010 or newer, at least)


So, in short, Mac Mini 2010+, 4G, better 8G of ram. First hit online sais 260$, so that's around your budget.