You can apply to as many companies as you want within 14 days and have it only count as 1 inquiry.
I have always used Dealership financing and everytime received a better rate through them then anyone else would have given me.
My advise is not what others give, but I always had good luck with dealerships. With my first new car purchase my credit score was about 650, they quoted me 8.99% and I signed with 5.99% on an $18K loan with No money down.....