STM32F7 won't run Linux. Use that MCU series with your favourite RTOS (e.g. FreeRTOS that is supported by the STM32Cube tool, this also provides kind of driver support for the internal LCD controller) or no OS at all. If you've never worked with an embedded MCU like that, it'll be a mess ... At least you have all the driver support for I2C, SPI, UART available from the Cube tool (although this doesn't always work as expected and you'd have to deal with DMA / IRQ channel assignment manually).
For embedded Linux, have a look at the STM32MP1 series, here you'd get all the typical Linux stuff. You'd have a working TCP/IP stack, display drivers, mass storage drivers and most probably working serial comms (UART) through the usual Linux devices. For connecting sensors through SPI / I2C I don't know if or how well implemented drivers (kernel modules) are available.