considering that you want only 3 games then it have to be titles that will last a little longer than standard next gen action games, right?
then i say:
Monster Hunter 3,
Metroid Prime 3,
Rune Factory Frontier,

Don't listen to them; listen to me, read my words and let them touch your soul, feel the burning drive within them, these words words of mine burn with an awesome fire:

No More Heroes

Maybe Monster Hunter  Tri and maybe Valhalla Knights: Eldar Saga

(+1 to anyone who knows where that's from)

I strongly recommend Bully. There's nothing like the satisfaction of throwing someone to the ground and stomping the crap out of them.

Try

1. Fire Emblem: Radiant Dawn, SRPG but easily my favourite game on the Wii, very challenging.
2. Metroid Prime 3, not exactly a shooter but a great single player experience in a first person perspective.
3. Try Madworld, its a cool game that uses WIi mote very well.

The bold describes Metroid Prime 3 pretty closely.  Although portions of the game are more about exploration.

Punch Out!!
Disaster: Day of Crisis
Geometry Wars: Galaxies

Metroid Prime 3
Conduit
Monster hunter 3

Hopefully that should fit your needs. You got your FPS, your old school nintendo, and a rpgish game. You could replace monster hunter 3 with Crystal bearers if you like square's stuff better.

Ok, since you have a limited budget I will recommend (prices from amazon uk):

-Metroid Prime 3 (£29.99), First Person Adventure, Nintendo Franchise.
-No More Heroes (£9.75), Action
-The House of the Dead: Overkill (£22.90), On-rails shooter, local co-op.

If you have more money you can wait for The conduit (june for £29.99) or Muramasa the Demon Blade (septembre, price not available).

1. Metroid Prime 3
2. Little King's Story
3. Punch Out! (maybe)

The Conduit
Monster Hunter
Cursed Mountain.