When you think about it, drills started as cordless drills. To be honest, they didn't even have electricity in those days. Even today, the old Brace & Bit can be the right drill for certain jobs.
What is the best all around drill for household use? 3/8 inch, variable speed, reversible.
3/8 inch is the size of the largest shaft that can go into the chuck and the largest size hole you should try to drill in metal without overloading the drill. For wood, you can get all kinds of larger drills with 1/4 and 3/8 inch shafts.
The variable speed is primarily used to allow you to drive in screws.
The reversible is primarily used to take screws out -- and to reverse wire wheels for cleaning iron railings. Change the direction of a wire wheel every 30 seconds and the job goes much faster because the wires are always cutting into the surface rather than bent over and just polishing the rust.
Battery operated drills are lower power than wired drills, but they are easier to handle, even easier to hold with their smaller and better balanced handles.