There is a simple answer to the best way to play Fallout: New Vegas, but the answer itself isn't what I would call simple or easy. The best way to play this classic RPG is on PC and with a ton of mods. Thankfully, there's a very handy guide out there that I used recently to turn New Vegas's somewhat messy PC port into a fine-tuned experience: The Viva New Vegas comprehensive mod guide.
He has really pulled this off to a level of brilliance where an entire functional PC setup - with motherboard, GPU and the SMPC - is consolidated inside of your chair.