For the budget, you might be better looking at "2nd tier" bikes, yes, Specialize, canondale, Kona etc. do some good stuff in the entry budget market but people like poseidon do great things in the same budget range.
The poseidon Red wood flat bar (29lbs - gravel) or flatbar X (25lbs - hybrid) comes the similar equipment (groupet, brakes) for 1/2 price.
Alpkit sells the sonder camino flat bar.
I don't know what the US equivalent of Planet X is but its worth researching.
Look into liv too as it s the female specific range from Giant. I know a lady who loves hers after spending many years on non specific bikes.
Either way, I would go with large tyre clearance (50-55C) for comfort and then fit tyres that suit your activities (large slicks/large hard pack/large knobbly). Note that I am faster on my test loop with continent speed king (50-584) than I am with panaracer gravel king slicks (35-622).