Which timer is the best choice for RTX RTOS?

I have found a variety of timers and wonder which one I should use for my RTOS application. I should run a non-timing-critical task periodically. I found the GPIO timers on the Cortex M3 as well as the SysTick timers. Then there is also a virtual timer that is offered by the RTOS itself and described under Timer Management.

My assumptions are:

• GPIO Timers are best for timing critical applications but can't be configured via CMSIS
• SysTick is a standardized timer from ARM, which is the same on all Cortex-M processors and thus easily configurable via CMSIS. It works with ticks and thus the best choice for an RTOS
• Virtual timers are thread-based and probably waste the most processor resources, because they are not hardware-based but provided by the RTOS.

Then there is also the question about the interrupt. The ISR should just check connections every few seconds. There are NVIC Interrupts and I could just define a function in the SysTick handler. My application already uses a UART callback interrupt that should definitely have the highest priority.