What class of license do you have? What band or bands do you plan to use?

To get that kind of range you're probably looking at an HF rig; the one I'm lusting after is the Icom 7000 or possibly the Yaesu FT-857D (US model numbers, don't know if Canadian market products are different).

You can do it all in a man-portable (not handheld) format with a Yaesu FT-817.

The right antenna is absolutely critical for any sort of DX application. It's even more important in mobile and QRP.