Express Action Sports

Probably the orginal Xbox for most games.
References :

For Classic get the N64
for Modern get the PS3, even though i’m a very big xbox 360 fan, the ps3 is great for solo and beginners
References :

NBA Jam came out for the Snes so for sports I would recommend that for "Starting Gamers"

For RPG Gamers the Snes and PS1 had more RPGs then the xbox, xbox,360, gba, nds, 3ds, wii, wiiu, and ps3 combined.

For shooters I would recommend Golden Eye on the N64 since it’s what sent the FPS from indie to mainstream.

For Online gamers I would recommend PC because it supports every MMO out there.

For Platformers I would make them go back to their roots with either sonic on sega or mario on the NES

For Turn Based Strategy I would send them back to basics with Shining Force on the SEGA

For Survival Horror I would put them on the PS1 for Resident Evil 2.

For action adventure Link holds the crown on the N64.

For racing Gran Turismo 1 on the ps1 would be a good start.
References :

I’d suggest the ps2 has most of the same games as the xbox does and some xbox doesn’t and can play the ps1 games too 🙂
References :

I’d reccomend singning up in vizzed,com, instal the plugin and then start with an RPG. Final Fantasy 6 or Chrono Trigger are great games to start with…
References :

The Sega Mega Drive has the best selection of retro games across the board in my opinion, games like Eccho the Dolphin, Sonic the Hedehog, Road Rash, Streets of Rage, The Lemmings, Goldan Axe, NBA jam etc are just a few covering most catagories and will keep any new or old gamer entertained.

Other worthy mentions:

N64 (Conkers Bad Fur Day, Goldeneye, Super Mario 64, Super Smah Bros)

Dreamcast (Sonic Adventure, Crazy Taxi, THPS2, Soul Caliber)

Snes (Super Mario All Stars, Super Metroid, Mario Kart, Earthworm Jim)

And lastly the PS2 for obvious reasons but all the consoles out there have something great to offer ether way, out of current platforms the Xbox 360 would be my choice.
References :