My friends and I are traveling to Shanghai(SHA) from Chicago(ORD) by way of Beijing(PEK),

leaving ORD on Arpil 2 and landing in SHA 10:55pm Arpil 3. We wish to immediately fly to Thailand, hopefully Phuket City(HKT). Unfortunately, timing and connections seem to be extremely difficult to navigate with Visa's. We land in PEK at 5:50pm(4/3). Which visa's could we use, and how long do we have to get out of China? Also, in the case of our flights to HKT, would we need to avoid connections in China?