Ripton,
It's really impossible for me to say. First of all I don't know what potential the instrument has to begin with and there are so many factors that can change the sound. One of the biggest changes could be made by working on the soundpost and if you have the capability, changing it. Chances are that the sound post is not fitting correctly (I've seen many hundreds of cheap violin sound-posts) and cheap wood with few grains. Next is the bridge. I'm sure you've read enough posts about cutting a post and it's affect on the sound. Strings play a little role on the sound but Helicores can sound great on a violin. From what I heard, you probably need a synthetic core string to warm up the sound a bit. At this point the choice would depend on your budget for this instrument. If you are ever in Florida, pay us a visit and we'll gladly look at it for you. It takes us a few seconds to take out and put back in a sound-post. Making a new one goes quickly as well but we like to experiment which takes much more time.