Which should I get first, an inspection or an appraisal? Great question!
It's important to understand that the services of inspectors and appraisers are pay-as-you-go and non-refundable. Unlike working with your agent, who is paid only AFTER you have successfully purchased the home you want, these contractors are paid in full and upfront. So the thinking goes-- if a buyer is to risk $350 or more or each, then it makes sense to decide which one might be more of a deal-breaker, and complete that one first.
A few years ago, when we were in a "traditional" market (hardly any bank sales or short sales) it was customary for buyers to get an inspection first. Then, once the request for repairs was submitted, if the seller responded favorably, and/or the buyer decided that the condition of the house merited continuing with the escrow, the buyer would then have his/her lender order the appraisal.
In this market filled with short sales and bank owned homes, appraisals are coming in all over the board, and many homes are not making appraisal, even when the comps appear to support the value. Part of this reason is timing-- since short sales take so long, the value at the point in time when the buyer submitted their offer, could be drastically different than the value months later, when the bank finally approves the short sale.
Particularly on newer homes, or homes which appear to be in very good condition, many buyers are electing to get the appraisal first, before the inspection. If the appraisal comes in low, and the bank refuses to renegotiate the contract price, then they've only lost the price of the appraisal, instead of paying for both.
If the home is in rougher condition, you may wish to get an inspection first, because if the repairs are more than you want to contend with, and the bank holds steadfastly to their typical AS IS policy, then you'll only be out the price of an inspection.
It does cost a bit to be a buyer. Both inspections and appraisals give you extremely valuable information. And if you have to cancel escrow, it's worth it to know the detrimental aspects of the home upfront, instead of making a very expensive purchase and paying for it for the next 30 years.
La Mesa, CA San Diego, CA