Do I need a pump to move rainwater from a tank to point-of-use?
It's going to depend on how much pressure you want and how high your cistern is with respect to point of use.  Typical US residential water pressure is on the order of 40 to 80 PSI.  One foot of head (height of the water column from cistern to tap) gives you 0.433 PSI, so you would need a 92 foot head to reach 40 PSI.  This is the concept behind water towers

You may not need that much pressure - it will just take longer to fill the tub, etc.  Whether that's acceptable is a judgment call on your end.