If you want to stay at or under $100, and still have a really good station, go for the Hakko FX-888. The Hakko FX-951 will get you what you want, but is 2.5x your budget to get an LED readout and the extra features (heating element is in the tip, not part of the iron's handle for this model, so it may perform even better than the FX-888 in regard to recovery time).
As
T4P indicated, Weller's QC has declined quite a bit, even for the German made models (WESD51 = Mexico, WD & WX series = Germany, and they all have DOA's and other failures). When mine dies, I'm going with something else, probably JBC.
The Aoyue will meet your requirements, but it's not at the same quality level from what I'm reading as the Hakko or others (heat shield issues; seems it may be fixable, but you shouldn't have to; long term reliability is unknown, but I'd think questionable; stand that actually comes with it doesn't seem that good either). Take a look here for the actual stand:
http://sra-solder.com/product.php/6510/0/soldering_iron_holder_for_968 to see what some of the comments are on about.
I wouldn't recommend skimping on an iron, so if you can't live with the manual knob on the FX-888, then save up additional cash for a better unit with digital controls IMHO.
Hope this helps, and good luck.