You've to search for car movers who will provide you with the quotes. They may allow you to put up to 100 lbs inside your car.

u can move your car by uship ,i have used it and u can put stuff inside .
about furniture use upack , call them and tell them other company is offering low rate than they will give u discount, it worked for me .

I do not need to transport any furniture, I basically need to transport 6-7 baggages around 50 lbs each, and couple of guitars and a musical keyboard. Any suggestions for cheap ground transport? I am ok with it taking a week for transport.

Upack and uhaul quoted me more than 3000, so I am looking for something cheaper.

Try greyhound. They move luggage too for cheaper rate.