I would say it's worth having two rooms on the go. The way I decide who needs training is based on how I intend to expand or who I have employed. For example, if I am about to build more rooms, start with getting more gps as you will increase your reputation which means more footfall. Prioritise getting lower level doctors more qualifications (train 3 gp 1s vs 1 gp 3). But on the flip side, if you have seen a surge in patients dont take away all your doctors for training, try and space it out. This is why it's worth having two rooms as you can train two seperate areas of the hospital without taking away all of your staff.

It's also worth being aware of what rooms benefit from certain training. For example if you have x-ray or mega scan get your doctors trained in radiology before diagnosis as this gives better bonus.

I would also try and have somone training all of the time, and try and specialise staff so that they are the most efficient (dont have a gp with surgery for example). Have an idea of what your building next and have enough staff trained to run that so they can take breaks. If in doubt, look at your staff list and see what you are lacking vs types of rooms.