Yeah the Wii U practically has a Wii built-in, all Wii games and accessories can be used. Even many Wii U games can be played with Wii controllers on Wii U (check compatibility per game).
The Wii U has some new games that are similar/sequels to Wii games, such as Wii Sports Club, Wii Fit U, Mario Kart 8, Smash Bros.U, Super Mario 3D World and New Super Mario Bros.U to name a few.
Wii U games look much better than Wii games, as the console is "HD".
The tablet controller is much like a regular controller but with a screen in the middle of it, which is great for playing games when the TV is in use. There are a very small number of games that require use of the GamePad Screen (Nintendoland, Deus Ex, WiiSports Club - Golf, and some levels in Super Mario 3D World). Generally though, you can use the GamePad as a controller and just ignore the screen. It's simple enough to use don't worry.
The battery life of the GamePad is around 3hrs, but you can plug in the charger cable while you play.
Besides the fact that Wii controllers (Wiimotes etc) can be used with many WiiU games, the official 'extra controller' for the Wii U is the Pro Controller (with a battery life of up to 80hrs per charge):
The Wii console and Wii games will obviously be cheaper than Wii U. Wii games were much about the motion/waggle controls, Nintendo are moving away from that with Wii U, but there's still some Wiimote focused games available on Wii U like Wii Sports Club and Wii Party U. But again - all Wii games can be played on WiiU.
Hope this helps and good luck!