Okay, the simplest form of what you’re looking for is the pipe command. It allows you to run multiple cmdline commands on the same line. In your case, the two commands are write `w` and execute current file `! %:p`. If you have a specific command you run for you current file, the second command becomes, e.g. `!python %:p`. So, the simplest answer to you question becomes:
:w | ! %:p
^ ^ ^
| | |--Execute current file
| |--Chain two commands
|--Save current file
One last thing to note is that not all commands can be chained. According to the Vim docs, certain commands accept a pipe as an argument, and thus break the chain…