I probably should've asked what the budget is too. As you've put cheap in the description, I'd suggest second hand.
Rather than looking for a brand, look at the components.
A matching groupset would be great. As a minimum, look for something along the Shimano Tiagra (or possibly 105 on a rigid) lines for gears. Deore XT (or LX) for brakes. Hopefully, someone, or a quick Google, will bring up similar kit for other brands. Nothing particularly wrong with lower spec kit, but it will be heavier and not as smooth. Higher level is lighter, smoother, more expensive and will wear out quicker.
Matching wheels. Any buckles, leave it, unless you can chip the price to replace. Decent wheel builders/repairers aren't cheap.
Frame and forks, check for damage and weight, but get what feels right.
As for brands, you can't really go wrong with Specialized, Trek, etc. Norco are decent. Personally, I'm a massive Kona fan, I've got four.😁
Have a look at CX/gravel bikes too. Even if you don't like drops, you can switch to a flat bar without too much expense.
Hopefully, someone else, whose bikes don't come from the 90's, will chip in with a modern take on bikes.😁
Good luck.