Definitely get your use out of the 3-month visa. The legality of teaching/working in this country has always been a grey area (a polluted, gassy, grey ether). Different provinces have different rules and attitudes at the visa bureau. Sichuan is considered one of the better places for attaining work visas – but hey, this is China. Could change tomorrow. If you can find a decent employer within the three months, and they like your style and (key point) you like theirs, they’ll get you a work visa. It may take one or two trips to Hong Kong, but you’ll be on the right path.
Like Miro said, be a bit careful. There are a number of shady schools who don’t care what your legal status is as long as you’re putting rich parents’ money into the boss man’s bank account. This is why on your 3-month visa, don’t be afraid to walk away from anyone at the first sign of monkey business. Be tough with them. They need you more than you need them. Don’t give them your passport, just photocopies. Mum is the word on your visa.
Ray’s advice above is priceless. “Come with an open mind and realistic expectations… Bring a sense of humor…” All three will be tested. Personally, I think I lost my sense of humor in this country.
@Charlie: But I go to Lanzhou for fun! ;D Trust me I’ll have the first ticket on the new train when it opens in 2027.