Well, the cheapest PC I've found is at Lowe's Home Improvement, right around $100. That doesn't include any pads or polishes, though, so that option is out - way beyond your budget.
There are a couple of cheap orbital polishers out there. I have one from Turtlewax I bought for about $25 that uses 6" bonnets. One of those, a couple MF bonnets, and Meg's DACP would be a good start after stripping everything off with Dawn (original, not any of the scented or anti-bacterial versions) and a good claybar. Most here will poo-poo these cheap orbitals, but for the price paid, they're amazingly competent. Is a PC better? Yes. You can vary the speed, and change the pads you use. Is a PC 4x better than these cheapo orbitals? I'm not so sure! But, with your budget, your choice is going to be between one of these cheapos, and doing it by hand. I'd go with the cheapo orbital. Polishing out haze by hand is not an easy task.
I've had Mothers and Zaino's claybars. The Zaino was more durable (held up over many more uses), but the Mothers was otherwise just fine. If you're new to claybars, you'll probably do something stupid like drop the clay and have to throw it out long before the clay has become unusable. I personally don't like using it with QD. I like lots of soapy, suddsie water to keep the clay from sticking to the paint. I think Zaino's instructions suggest this as an alternative to using thier QD with the claybar.
There are other good clay bars out there. Once I've exhausted my Zaino clay bars (I just retired one, and have another new one ready to go), I may try the Megs clay.
I haven't experienced hazing or smearing with the carnuba waxes I've tried (Megs #26 yellow wax in paste form, and Collinite 476S).
Good luck!
