Some years ago a movie came out: They Call Me Bruce!  In this comedy, an
Asian man made his way through a number of people who thought he was a
great martial arts Master simply because he was Asian, triumphing in the
end.  The moral is clear and directly applicable.  Do not assume that
because the instructor of a given school is Asian that he is, in some way,
superior to the instructor of another school who is not.  Skill in martial
arts is not inherent to any given "race." Likewise, do not make the same
mistake concerning the sex of an instructor.  There are many very talented
female instructors.

Don't let yourself be distracted by a fancy school or unrelated goodies
such as weight machines or saunas.  A well kept, safe training area is one
thing but extraneous features, though nice, ultimately only add to the
expenses of the school.  There are a good number of excellent instructors
teaching out of their garages, basements, and back yards.

Don't get distracted by uniforms either.  Many Asian martial arts wear the
traditional "white pajamas" gi while other martial arts have different
uniforms and some, no uniform at all, preferring instead "street clothes" or
comfortable, loose fitting training clothes.

Also, don't pay too much attention to numerous trophies and medals. 
Trophies are easy to come by in martial arts competitions.  On top of that
they are inexpensive and easily purchased by unscrupulous scam artists from
the local trophy store.  Though this practice is uncommon, it has been
known to happen.

Don't judge a school or instructor by how much they charge.  It's human
nature to assume that a higher priced product is going to be somehow
better, yet this is not always true in the world of Martial Arts.  Some
instructors are simply teaching for the joy of teaching and not trying to
make a living or any real money from it (more on this in the
rec.martial-arts FAQ).  Some arts and Organizations discourage their
instructors from trying to make money from instruction and will therefore be
inherently less expensive.  Yet other arts are the flavor du jour and suffer
from higher demand than there are available instructors, thus making them more
expensive.  As long as the price of instruction falls within the range that
you are willing to pay, don't worry too much about it.

Further, don't pay too much attention to lots of certificates in Asian
script decorating the wall, particularly if you don't read the language
they're written in.  Most instructors will display only the rank
certificate of their top rank (or the top rank they hold in each art
they're ranked in if they are ranked in more then one).  In general, this
should mean that there aren't many certificates displayed.  With the state
of current computer technology, it is easy to produce impressive looking
certificates that say anything you wish them to say, even that the bearer
is a high ranking martial artist.

Finally, don't be overly concerned with the rank of the instructor.  While
in the early stages of training in your new art (say the first 10 years)
you probably won't be able to tell the difference between a 3rd Degree
Black Belt and a 9th Degree Black Belt.