I have a 94 Spider. It has Hill Engineering 25mm spacers at the rear and I am told that makes a huge difference.
I am no track hero, but I have a massive amount of confidence driving my 348 and had a great time chasing an F40 over the hills from Siena to San Marino last year.
I am also a former Lotus Elise owner and I did push the limits with that car.
I know what you mean by the "all the weight behind you" comment. It does feel like a go-kart, and I once had it give a little sideways twitch braking into a corner (212 Export will confirm!)....but I think you get your head around that quite quickly.
I have P Zero rubber, but inherited those when I bought the car so have yet to make a rubber decision myself.
Ferraris : 1990 Testarossa, 2000 550 Maranello
Others : 1967 E-Type S1 FHC, 1972 S1 XJ6, 1972 Maserati Ghibli SS, 2006 Ford GT, 2001 Mini Cooper Sport 465/500
Past : 1980 512BB, 1994 348 spider, 1989 300 SL, TVR Griffith, TVR Tuscan, Lotus Elise, 996 Turbo, Cayenne GTS