I have a Grand Lodge Hunter fan. It has a remote control and no pull chains.
When I first turn the switch on, the light comes on. So far so good. Then
I turn the fan on with the remote. It starts turning backwards. I have
Reverse button so I can press it and get it turn the right way. However,
I'd like to have the fan turn the right way from the beginning. Any
Ideas?

Leave the wall switch on and control the fan from the remote. Many fans reset when you turn the wall switch off.