What you want to look for in secondhand furniture is good wood hiding under layers of badly applied paint or varnish. The more thoroughly its quality is concealed, the more valuable the piece will be when you're done. Many smaller items, and almost anything that is lightly finished, will be bid out of sight . . . so your best bets are the big gummed-up uglies.
Material, construction, and general appearance of old furniture are more important than detail or present state. I've even bought pieces that were failing apart, as long as the wood wasn't cracked and the joints themselves — as distinct from their shaky fastenings — were in decent shape.