The best single player Wii games for now:

• Mario Galaxy
• Metroid Prime Triology (or Metroid Prime 3)
• Super Paper Mario
• Zelda - Twilight Princess
• de Blob
• Super Smash Bros. Brawl (even the single player campaign is worth the money)
• Dead Space: Extraction
• Resident Evil: Umbrella Chronicles
• Wario Ware: Smooth Moves
• Lego Star Wars - The complete Saga
• Little Kings Story
• Rogue Trooper
• Mario Kart Wii
• Okami
• Resident Evil 4
• Fire Emblem: Radiant Dawn
• Muramasa
• Cursed Mountain
• Boom Blox Smash Party

WiiWare:

• World of Goo
• NyxQuest
• Sword&Soldiers
• Lost Winds 1+2

New Super Mario Bro Wii (next month, for sure)
Zack & Wiki: Quest for Barbaros's Treasure
Wii Sports Resort
Samba de Amigo
Okami
Little King's Story
Lego Star Wars
Mario Kart Wii
Excite Truck
ExciteBots
de Blob
The Conduit
World of Goo
Super Paper Mario
Dead Space: Extraction
Metroid Prime Trilogy
Wii Fit Plus
Muramasa: The Demon Blade
Klonoa

Endless Ocean

Fixed!

Yeah, if it's for your family I would suggest you get the whole 'Wii' game set (Wii Sports, Wii Play, etc.) and Mario Kart Wii. Some Wii-Ware games such as Tetris Party and Bomberman Blast are great fun also.

Really depends on what you like. Here's my list, in no particular order:

A Boy and His Blob
Little Kings Story
Metroid Prime Trilogy
Okami
Dead Space Extraction (can be played co-op)
Zack and Wiki
Muramasa
The Conduit
Dawn of Discovery
Lego Indiana Jones (can be played co-op)
Cursed Mountain (if you get the hang of the controls)
Resident Evil 4 Wii (even if you played it on another console)
Deadly Creatures
Tenchu: Shadow Assassins (opinions differ on this one)
De Blob
Mario Kart Wii
Excite Truck
Excitebots
Zelda Twilight Princess
NPC Pikmin
Shaun White Snowboarding (play it with the Wii Fit balance board)
Tiger Woods PGA tour 10 with Motion Plus
Punch Out
Klonoa

Minigames or not, you really owe it to yourself to buy Wii Sports Resort.

Wiiware:
World Of Goo
Swords & Soldiers
Lostwinds

Lots of VC titles (Zeldas, etc).

Coming up:
New Super Mario Brothers Wii
Resident Evil: Darkside Chronicles
Final Fantasy: The Crystal Bearers
Tatsunoko vs. Capcom
Silent Hill: Shattered Memories
Fragile
Arc Rise Fantasia
Red Steel 2
Monster Hunter Tri

Ah! it shocked me to see you were gonna get a wii... but in fact it's you mum, that makes sense.

I'll just confirm a few of the previously listed games:
Mario Kart Wii (that is the must have game, get as many wiimotes as brother/sisters you have)
Wii sports resort (2 wii motion plus is a good investment)
A Raving Rabbids game
RE:UC (2 players so it's fun with your brother or sis.... the second player does not need to be good as you share the life bar)

you'll probably want Wii Fit + for your mom/sisters (get the + rather than the normal since i's comming out now)

Games for just you, that really depends on your tastes ^^ but you should enjoy the ones above too.

If you like long games then any of these are fantastic.
Fire Emblem
Little Kings Story
Rune Factory

As for shorter games/games you can play in short bursts
Sin and Punishment (Sequal is comming soon also)
ExciteBots
Mario Kart
Sports Resort

Well since your probably not made of money I'll just name the must haves

1. Super Mario Galaxy
2. Super Smash Bros Brawl
3. Mario Kart Wii
4. Wii Sports Resort
5. Legend of Zelda: Twilight Princess