As others have said, most states won't charge you sales tax if you make a cash purchase. Sales tax is typically paid in the state you register the car. One favorable aspect I like about living in SC is there is essentially no Sales Tax on the purchase of a car. There is an IMF (Infrastructure Maintenance Fee) charge, or Sales Tax (depending on what you purchase & I've never paid the SC Sales Tax on any car I bought). Most people pay the IMF charge & it is 5% of the Purchase Price but can not exceed $500! And SC gives you 45 days to register the car from date of purchase. The new SC owner has to pay the County Personal Property Tax on the car before applying for registration at a DMV office. SC DMV won't even talk to you without a copy of that tax receipt. Tax on my 2007 Coupe is less than $50 per year. Keep in mind everything I've stated is for the purchase pf a car that the existing owner has a clean title to - no lien! If a lien is involved, there are service firms that act as 'go-betweens' between old & new owner to insure a secure transaction that protects all parties.

As far as driving the new car bought out of state to your home, as long as you have paperwork that's been properly executed & signed by all parties, you shouldn't have any issues. If stopped by any police, just show the paperwork. And like some have stated, I'd contact your insurance provider and have the new vehicle insured with an effective date matching the date of sale. That way you know you're covered.