I recently (after 9 years) got around to installing a Topeak rack on my old hard tail mountain bike. I'm also an occasional birder and like to take bins on some of my rides. I don't use dedicated bike bags but rather a Mountainsmith lumbar pack that I can wear or strap onto the rack. On rides, the bins I take are Zeiss 10x25 Victory compacts. Not the best birding bins but small and great for longer distance viewing (and light!).

Where I live and ride, a mountain bike is often the better choice. You can ride a bike like mine on pavement just fine but you can't ride a road bike on dirt all that comfortably (or safely).

I'd think any number of hybrids or comfort bikes that will take a rack should be fine for you.