I'm a big fan of Normal mono, and yes, dealing with fighting can be a pain, but it isn't impossible.
I usually deal with fighting types by using paraflinch Togekiss, or band/scarf Staraptor. Sometimes Porygon2 can even deal with them, especially if they're running Superpower.
I also use Sawsbuck as a counter to Breloom(until Techniloom is released), Whimsicott, Serperior, and other grass stuff.
Ambipom or Persian make great leads, and I've had success with a Scarf Smeargle lead.