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If you are really into embedded programming then the answer is probably "none".
Except for the Raspberry Pi (which may be a good entry point but can lead to bad practices), almost all of the microcontrollers I've seen or used are 'bare metal' - your code is the only code in the device.
Arduinos' provide a 'main' function and some library code that provides some code interfaces. However you really are very close to the hardware with these.
Also, there are some significant differences in the ways that an RTOS and and OS work.
Also can you explain what you are trying to do what makes you think you need to know about RTOS and Linux for embedded systems? (I'm not saying that they don't have their place in embedded systems, but what you want to achieve will help direct our responses.)
in my opinion one distro is good for embedded. It is "Gentoo Linux", because it is so called "meta-distribution" (if you want you can made is almost "from scratch").
The "Yocto" distribution is derived from Gentoo "emerge" and this Linux (yocto) is considered as standard in embedded linux applications. BTW: Yocto is rather a "build system" than pure Linux distro.
The first thing I would probably suggest to do is get yourself a Small computer like the others have suggested - Raspberry Pi, Beagle Bone etc which are based on Linux (if this what you prefer). There are plenty of tutorials on how to interface sensors, add drivers to existing kernels etc. (depending on what you exactly want to learn) for all these platforms so that should give you a good starting point.
If you are looking to learn more on embedded RTOS then you can have a look at micrium OS which is small sized RTOS. You might need more background on RTOS concepts before you start though.
There is no one particular way to approach learning embedded systems you just need to dive in.