If a big company decide to sue you, will they sue based on where the site is located or where is business is registered and operated?
They are going to sue you where is gives them the best advantage. If they are looking to collect damages, they are probably going to do where the site owner lives.
What is procedure when a company want to sue you... - They will go after your hosting company first or you directly?
OP, it depends what are they out for. On DMCA, the hosting company gets away with notifying you of the infringement and suspending your account. So forget about them taking the heat off you. If it's just a breach of TOS, things are muddier. Once they can legally force the hosting company to give them your details, they can sue you anywhere. Fake registration details and offshore hosting might help to protect from these, but you should know how to do it prior to engaging in any activities that could trigger such a response, right?
Very rarely will the hosting company be sued first unless they are repeat offenders or grossly negligent. It's your site. You are responsible for the content. You are the one in violation. You get sued.
They will choose the jurisdiction where: A) you have the most assets available, and B) history shows they are most likely to get a favorable judgment. The farther you're spread out, the more options they have.
I think to you.. i think depends on the case.. if they can sue the host then they'll go with the bigger fish first..