Should I fix my broken Laptop through Lenovo or Best Buy?

I recently cracked the screen on my Lenovo Yoga 3 14". Lenovo and Best Buy have the same type of policy. For Best Buy, I pay $35 to have it shipped somewhere but if I get it fixed with them, that cost is added onto the total. If not, then I lose that money. The same goes for Lenovo, except it is $99 instead of $35.

Which place would give me the cheapest price to fix my display? Also, which would be quicker?

Have you looked at Amazon or eBay to see if screens are available for your laptop? Changing a laptop screen isn't difficult, I've done more than a few, if you're looking for the cheapest route, doing it yourself is the way to go.