Shimmy can be caused by a tire out of balance, an improperly inflated tire, an alignment problem, etc.
As for the rust: simple surface rust on your undercarriage will not hurt the vehicle. Because it is now in Arizona, you won't be dealing with rust at all. The two vehicles I brought out here from New York virtually stopped rusting altogether. Unless the rust is very bad (i.e. rusted out brake rotors), you shouldn't have a problem out here. IMO, I wouldn't bother to clean up surface rust.
Gen1s are good vehicles. Gen2 has more power. I guess it depends on what you want the vehicle for. I use mine for towing, and I appreciate the bigger engine in my '06 (vs the '01 that I had previously).