I am a Wii fan and play a lot. I have not met any game that did not work with the standard remote, some might requite the nunchuck (one comes with the console, I believe).
You do not need any wheels for example for MarioKart, the wheel is a simple piece of plastic in which you put the normal controller. I suggest you to buy a second controller plus nun-chuck and if it is in the budget, a balance board. I have a classic controller as well, which was frankly a waste of money. I like the balance board and games that work with it. If you want to buy one extra game, go for "Rayman's raving rabbids 2" or "Rayman's raving rabbids TV party"... it is great to play around with all the functionalities of the Wii.