Simple sample project with STM32F303

I would like to use in a new project ARM Cortex M4 from ST, more STM32F303.
Can you recommend a sample project with this processor, a project which would see minimal involvement of the MCU,

How about using ST's Discovery board for getting familiar with this MCU: https://www.st.com/st-web-ui/active/en/catalog/tools/PF254044
These boards are pretty cheap (11 $), conatain some sensors, LEDs etc. and the onboard debugger ST-Link.
There's a firmware package available with 28 examples.

Discavery know, I thought something else, something that puts more emphasis on the analog part.

The Discovery board supports the STM32's analogue to digital converter, which is very good. You can hook anything analogue up to the breakout pins, and then you have analogue signal as digital data. So pick a sensor, really - or just build a simple voltmeter.

But ultimately, if you want to do a microcontroller project, you're going to involve the microcontroller to some degree. Your best bet getting started is going to be picking something like the Discovery board that has tons of sample projects, build tools, startup files, etc. already done and available from ST. Any other projects I can recommend first require at least a basic knowledge. So start with those samples, and use them to learn.

For instance, Blinky is a sample project that simply blinks the Discovery Board LEDs. You could then adapt that to make the LEDs blink every time voltage data comes in over the A2D (although you'll want to read about the A2D's functionality first).

So my point is, even using the MCU minimally requires learning how it works, even if just at a basic level.