Either is fine. It doesn't matter which brand you use, or if you use DOT 3 or DOT 4, as long as you change it regularly. Honda says either every 3 years regardless of mileage, or some of the newer Hondas have a code in the MM for brake fluid. But you can get away with replacing it when you do the pads and rotors.
Walmart brand DOT 4 is $5.74 a quart. You can get that one, or another brand on sale somewhere, so nothing wrong with stepping up to DOT 4 with the higher boiling points.
It seems your pads are about half worn.