For me it has to be a sport, tinted windows, lower suspension.
SE maybe smoother ride (only upside i can see to having a SE)
Cant help with the top mount heights as i've just sold mine so cant look for you.
No idea about the auto with buttons, never driven one, cant help you there.
AS for probs, i've never seen a rusty IS200, sure there has to be a couple about tho.
CD player is $hite so budget for a new one, alloy's are a problem with peeling / corroding so budget for a re-furb or change, apart from that, they are bullet-proof.
The only prob with IS200 is performance, they are not slow, but no too quick up the gears & tuning is expensive, £2K for a decent supercharger.
I am not sure but i think the altezza has the same interior as a S model IS200, not as pleasing a place to be as a SE or Sport, but the engine will put a smile on you Face.
For up to £3K, dont expect too much of a car, i just sold my 60K mile, 2002 Sport with TRD kit, Sony satnav & dvd, 18" wheels & loads of extra little touch's for £4.5K.
Happy hunting, let us know how you get on.