Recommended current for external breadboard power supply
I suggest you buy a 5V regulated adapter for your ~1A requirements. A standard adapter (or power bank if you want battery power) and use the USB socket rather than the barrel jack.
Similar (but not interchangeable) boards with the same part number are available with a mini or micro USB socket to match standard power supplies as used with Raspberry Pi, cell phones etc. Make sure the two are compatible, there are a number of combinations. The USB power connections are connected directly to the +5/0V and nothing else.
This will avoid excessive dissipation on the board, and help prevent oopsies that can destroy your parts.
You can use the power supply module you linked to create a 3.3V bus if you need it. The 5V from the USB socket is passed along directly when switched on. See my answer here for the schematic of a similar product sold with the same part number.
Note that the one you've linked does not include a resettable fuse, which I would consider at least an advantage if not a 'must'.
As another detail, it would be nice if the polarity of output matched the color of markings on your breadboard (red = +, blue = GND), but most seem to be reversed.