PaulRivers

It's true that for most people they can ride a bike that's one of two sizes in the bike size lineup if adjusted properly - like they could ride a 54cm or a 56cm and be fine with a decent fitting and adjustments. However, it's also true that the #1 mistake I personally see people make in buying a bike is buying the wrong size because "it's a good deal", or because the shop wants to sell them something in stock and they only have the wrong size in stock.

The cheapest way to go is a flat bar bike. At entry level, it's usually about half the cost to get a flat bar vs a road bike.
Decent Entry Level Flat Bar: $400
Decent Entry Level Road: $800
Decent Entry Level Cyclocross: $1,000

I think you're 100% right that if you're riding any actual dirt roads, you want to be able to accommodate a fatter tire. I've tried riding my 23c road bike on Iowan gravel roads, lol - it doesn't work for more than just crossing the road very awkwardly.

Generally you'll be a little faster on a road bike than a flat bar bike, but not hugely so. Your fitness level will make a bigger difference.

Some "road" bikes do come with cyclocross level clearance fyi - like the Specialized Sequoia.

I would ask why you want disc brakes - they are better if you're biking in the wet, but otherwise on a relatively skinny tire bike they don't make much of a difference. They add some cost, and hassle if they start squealling when wet or the slight rub most have (in my experience) is annoying to you.

I wouldn't worry about clipless pedals and shoes at your price range. They make maybe a small difference in riding power (it's debated a lot whether they really help, with studies of pro cyclists even), but I'd get decent flat pedals like these:
Robot Check

And I'd rather spend my money on faster rolling tires than clipless pedals and shoes - at your price range.