Both the regular and express trains pass through Jinan.
If you are coming from Qingdao, regular trains run to Tai'an and take 6 hours while costing ¥56-65 one way. Express trains also run from Qingdao and take only 3.5 hours, though the ticket price jumps to ¥148. Purchasing your train ticket in advance is a must during busy season, unless you don't mind standing in the aisle for the entire trip.
Alternatively, you can also take a bus from Qingdao's Sifang long-distance bus station. The trip takes 6 hours and costs ¥116. Unfortunately, it is virtually impossible to figure out the bus schedule without going to the bus station (there is no number to call and nobody in town seems to be familiar with the schedule), but Sifang is a short cab ride from town (only about ¥12-15 from the train station).
The holy mountain Taishan (Mount_Tai).
Tai'an's urban areas are generally safe at daytime, but it's still necessary to be careful of pickpockets in crowded areas. What should be especially cautious is, suburbs and country roads in Tai'an can be extremely dangerous, as they become the heaven of robbery in several decades.