There appears to be some stains indicating seepage.We just did this kind of foundation repair on a house with steel beams 6 ft oc with an interior moisture barrier and an interior drainage tile with a sump.  

Tile would be great, but possibly the noisiest option (impact noise) and the kitchen is right in the middle of the floor plan.I treated the sub floor to reduce noise, but am now considering laminate or even vinyl (due to better moisture resiliency).Is tile going to be much louder than the current existing sub floor (at least in terms of impact noise).

Obviously it rains a lot here and you can definitely smell the moisture smell when you first walk in.

Metro areas which do not experience hard freezes or significant moisture.

I believe that this can lead to termites and extensive moisture damage in the structure of the property.

This tends to lead to mold, rotting floor joists/sill plates, and other moisture based damages and problems.

I would love some cheaper design ideas for the basement, but I want something that will stand up to moisture issues.

I assume accommodations got a little crowded :)Two problems:1) Water bill goes out of sight2) Lot of extra moisture from too many people in the unit means more likely to get mold. 

I have used DE inside for flea and tick treatment with some success but keeping your yard tick free in an area with grass and high moisture probably not going to happen.

Are you certain there's no new potential causes of moisture in the home?