Development using Arduino...

I'd go with external SPI interface part then, either EEPROM or FRAM (ferro-electric RAM; has SRAM access speeds, EEPROM data retention but without the write limitations/byte. Mouser.com has a good variety of them). Store as much as you want per logged event.

I use FTDI in my projects. No messing with additional programming of 16U2 part for a USB interface.
I add a socket to plug one of these in and not mess with soldering the TSSOP package down:

MIKROE-483usb_uart.jpg

maverickpilot:
Does this make the board native USB?

"Native USB"? That's an odd phrase.

So instead of a virtual com port the computer will recognize the board as a USB device?

Virtual com ports are a particular type of USB device. But I understand what you mean.

Like when you plug in a digital camera, it'll say "Sony DSCXXX" or when you plug in a phone it'll say the brand and model number?

Exactly. On this forum, MIDI and HID (keyboard or mouse) seem to be the most commonly mentioned USB devices. It is possible to mimic any USB device (e.g. storage, camera, joystick).

And at the click of a button the current reading should be stored along with the time and date info.

A range of days with a granularity of one second. If two bytes is used the range is about 3/4 of a day. Three bytes gets a range of 194 days.

Two bytes for the value plus at least three bytes for the time-offset with at least 1000 values stored means you have exceeded the available EEPROM. It's time to shop for a FRAM.

...oh, wait... Are you going with the 2560 or the 1284?