I agree somewhat that using a stick instead of a wheel for steering can be easier when you get used to it (because of near-instant opposite lock), but the fact is there's a massive difference between buttons or triggers and pedals. When I use my pad I usually have to have TCS and maybe even ASM on when I drive a more powerful car; my 620bhp 458 is about the fastest thing I can drive without aids and not spin, but as I'm on the extreme events there's just no way I can drive the 88C-V or NASCARs without aids as the wheels spin far too easily, but with a wheel you can be far more progressive with your controls and there's a million more levels of pressure you can explore if you use pedals, you can even turn ABS off in some cars...!
Not to mention the immersive aspect, of course; you're driving a realistic representation of a car, so why not use the same controls as a real car? That said, the H-pattern shifter and clutch are nice, but not essential to the wheel experience, the Driving Force GT or even a Pro is a great wheel if you don't want to spend loads, I'd estimate the GT at $120 (they're £80 here). I have a Driving Force Pro, picked it up second hand for £30 and it's lasted me 5 years so far and is easy enough to fix when the pedals go funny.
You might find it takes a while to learn to use the wheel (most people can't tell, at first, whether they're supposed to fight the feedback or let it control the car), but once you've gotten used to it it's so much more fun than the pad.