Transit through 2 airports

Indeed, you do not need any kind of visa because your entire transit will be accomplished within 24 hours. So, you will be covered by 24 hours visa free transit. Please, just use correct terminology because this is not 24 free transit visa, but 24 hour visa free transit, so there is no any visa involved here.

Your layovers are short and it is not a problem with a layover in Guangzhou, but the one in Beijing could be a bit problematic. In any case, the first thing when you land in Beijing will be to approach 24/144 hour visa free transit where you will present your flight tickets. This application is free of any charge and the permit will be granted and you will head to the immigration because your next flight is a domestic one.

When you arrive at the 24/144 hour visa free transit counter, you will have to ask for a priority in order not to lose your flight to Guangzhou. Please, just be among the first when exiting the plane in Beijing and also just be open and ask at the counter.

I am more than confident that you will be able to accomplish all your formalities, but if you feel somewhat insecure, then a transit (G) visa might be of help because you will skip a visit to the 24/144 visa free transit counter. If you decide to obtain a transit (G) visa in advance, you will fill out the arrival card that will be dispensed on board the plane before your landing in Beijing and you will tick the box on it - transit. After your landing, you will head directly to the immigration to catch your connecting flight to Guangzhou.

If I were you, I would be going for a 24 hour visa free transit, because if you are agile and know how to ask for the priority that will be definitely given to you, you will manage to catch your flight to Guangzhou as well. In any case, I wish you a successful journey.