Premium for shorter lease?

[Luke H.]

Happy Holidays from Texas!

New house, totally remodeled, potential tenant is asking for 6 month lease, with month to month after lease ends.  I prefer 1,2,or 3 year lease.

a) Should I charge more for a shorter lease?

b)Is that common and legal?
b2) If so, how could I determine how much more? 

The area has rents are all over the place, so hard to determine.

Can I require them to have renter's insurance?  They have a dog and want to make sure I am covered.

Thanks