It sounds like you may want to look at an Epiphone dot, which is the epiphone es335, or any semi-hollow epiphone.

I actually have seen a semi-hollow Les Paul before, it was an Epi na d I know it was a regular production model,but I havent seen one around for a long time.
With semi-hollow electric guitars, you can make some noise with no amp, but the guitar is built for use with an amp.

Also look into the Ibanez artcore series...they are awesome guitars and are very affordable.