Re: classical guitar under 600$
takamine install adjustable truss rods. The yamaha electro classicals do also.
Its not really a big deal for classical tho. A high action gives greater projection. Super low actions are not conducive to good nylon string tone. The necks are also very beefy and under a lot less pressure than even the lightest steel string guitars. Treat the guitar like a person (i.e dont leave it in the car on a hot day, or leave it out in subzero temperatures) and it will stay happy for many years.
As far as solid woods go, you can get a solid top and back, but its pretty unlikely to get solid sides at that price point.
As far as electronics go, if you spend 600 bucks on a pure acoustic, it will be a nicer axe than a 600 dollar electro acoustic. YOu can always install a pickup with an outboard preamp which means you only have to drill a hole for the output jack and a tiny hole under the bridge saddle (fishman are nice) later if you want to play live without mic.s. Piezos sound pretty awful recorded, so a mic is still preferable for home recording.