Very good chance that a type rating will be done 100% in the sim (unless it's a DC-3 or something).

Who pays for it? It depends. Typically if the company pays for it, you'll have to sign a contract so you can in effect work off what they spent on you. Some airlines like Southwest want you to have a type rating before you even think about applying.

Most type ratings will be $10,000+. I believe ERJ's and CRJ's are around $15,000.

-Brett