All the STM32F0 that I can think of come with UART hardware – meaning that you just need to write your string to some address, and trigger the transfer.
The knowledge of how to do that can be taken from the Reference Manual of that family (ST Document number RM0008), or just straight from the UART driver within the STM Cube software package.
Electrically, you'll really get a TTL UART – any TTL serial-to-USB converter will do. The Nucleo boards just contain a second microcontroller that plays a USB-to-STLink and USB-to-TTL-UART bridge.
For "easy" debugging, the UART is certainly the least error-prone communications interface in the chip. If you're tempted to directly communicate with the PC: Your MCU comes with a USB2 transceiver. You can, adding a few resistors, directly connect that to your PC, and let it look like a serial adapter itself, just giving you your messages or data! That is, given you have a firmware that handles the USB stack. ST offers a library to do that, and that comes with examples. Be warned though that USB is way more complicated than UART, and if you just want to occasionally print short strings, UART certainly is sufficient. The USB interface allows you to send USB data packets through USB2 Full Speed (that's the 12Mb/s standard) – that can be hell of an advantage if you need e.g. to build something that samples a signal rapidly (that's why I used USB on an ARM the first time) in the long term.