For non-members, the return policy is 15 days. For elite members, it's 30 days. For elite plus members, it's 45 days. In order to become an elite or elite plus member, you have to sign up to retrieve points, and then you accumulate points through purchases. The more you purchases, the higher your member status. Then after so many months of inactivity or insufficient purchases, the status decreases.
If you're not a member, then you'll have 15 days to return the TV after purchase. In my experience, Best Buy has kept my receipt electronically in their system. There's been a time or two where I forgot it and they were able to pull it up. As long as they're able to verify the product is theirs, you probably won't have a problem. Still, you want to keep your receipt. When you do make a purchase, however, ask for an electronic receipt e-mailed to you. You can't lose those and you can pull them up on your cell phone!