What's the cheapest and quickest way to travel from Shenzhen to guilin?

I'm afraid it is hard to achieve both of your targets at the same time: cheapest & fastest. Actually, the cheapest way is the direct train between, but it takes around around 14.5h; the plane between is fastest, but is more expensive than trains. Anyway, if you travel in slack season, the air ticket may have great discount. Just have a check!