"In General" Shimano RD from 6-9 speed mountain & to 10 S road will interact just fine with 6-9 Mt & 6-10 road shifters. The shifter and cassette speeds have to match, derailleur doesn't care. There are certain exceptions that really don't affect your situation
Front Derailleur typically a Shimano mountain needs a Mt shifter and road a road shifter. You can always try and see if what you have works and if it doesn't move on to match things.

You'll probably want to use a shimano HG freewheel for best results.