it depends on the followings:

- what's put in your contract?

- what will you purchase? If your bidding top dollar you may want do as an extensive of an inspection as you can do on your own before signing the purchase agreement then do the appraisal 1st, if you are buying a distressed property at a low to middling price do the inspection 1st. If you are buying a fixer at top dollar, flip a coin and cross your fingers.

both are contingencies. Buyers back out for both low appraisals and inspections issues. home inspection is MUCH cheaper than an appraisal--typically. hence, most buyers do inspection first.

just my 2c.