I hoped that someone can direct me as to where to take the coach from Guangzhou (railway station or somewhere near the subway station) to Shenzhen Bao'an airport.
As far as I'm aware there's no coach direct from GZ to the airport in SZ. The best advice I've had from people who have made the trip before has been to get a direct coach to Luo Hu and then change to a special airport service coach.
For all it's worth - possibly not much - but there are buses from Guangzhou to Bao'an, though that's not exactly Shenzhen Airport. However, a bus trip to Bao'an saves you potentially a one hour bus journey from Shenzhen Train Station (or the bus terminal there) to the airport.
A quick taxi trip would set you back a modest outlay for the short trip to the airport.
Cheap accommodation in Guangzhou? I can't give you websites, but I would try a hotel near Guangzhou Train Station on Huanxi Xilu (there are a couple that are not pricey as opposed to many on the far side of the station square that charge five-star rates).
BUt in the off season you can easily get published rates down to an affordable level.
As we have time to kill and the frequent buses from Liu-Hua bus station were to Lou-Wu , we took that , did some shopping & had a meal. thereafter a RMB20 ride to the airport from Lou-hu.