Firstly, what engine do you have? Is it a V6 or a TS? This will effect what parts can be recommended.
But in general, to reduce body roll, upgrade the front and rear anti-roll bars. Ultra Racing offer a rear ARB but they're generally pretty expensive and I'm not sure if you can order directly from them any more (Alfa Romeo Spider GTV Rear Anti-roll Bar / Rear Sway Bar / Rear Stabilizer Bar - Ultra Racing Product Catalog
). I have never heard a bad word about the ultra racing ARB though, so its definitely quality. Some people have also fitted a front ARB on the 3.0 from a 145/146 as its quite a bit thicker. I think in your case, the front ARB is the most important one to change to improve the body roll, but changing the rear definitely won't hurt either.
To reduce shaking you will be pretty much forced to stiffen and uprate the suspension to a stiffer setup. I know you said you don't want to stiffen it but if you want to reduce shake, its really your only option aside from adding roll bars or a hard-top. Either way, even if you do stiffen the suspension, you will always have some shake in the Spider, though with stiffened suspension it should be significantly less.
You could do so by powerflexing the rear end, pairing some Koni sports with an OE spring or Eibach lowered springs (stiffer). I suppose you could try using OE shocks with a stiffer spring if you could find one. But unfortunately, without stiffening the suspension, you won't reduce the scuttle shake.
But like I said, we need some info on your engine (V6 or TS) before we can recommend specific parts