Before anything else, make sure everything you have is in good condition. I see lots of people spend money on new performance equipment before the inspect their suspension to make sure everything is in good shape. Links break, bushing wear out, shocks leak. Make sure you knwo what you have in the first place.
If handling is your weak spot against the e-type, start with tires. I really cannot emphasize that enough. 185s fit well, but some people go as far as 195s. You might experience some rubbing with those. Don't just buy any tire. Check the wear rating and get the lowest rating you can tolerate. The lower the wear number the softer the compound. They stick better but wear faster.
You want wheels that will carry the wider tires. If you need new wheels to carry the wider tires then think about alloy wheels which will reduce your unsprung weight.
The cars are designed and constructed with positive camber. This is unadjustable without modification. For street purposes, you can take care of this with off-set upper a-arm bushings. There is an active thread about this on the board right now. They will give you as much as 2 degrees of negative camber which is plenty for road use.
Then you need a good alignment. Make sure you have a bit of toe in and one to two degrees of negative camber (with your new bushings).
Now stop! Drive the car in controlled circumstances and see what it does. I recommend and autocross. Determine the right tire pressures for maximum performance. Figure out which end of the car breaks away first. It the car understeers try varying the tire pressure in the front end. If it oversteers, vary the pressure in the back end. If you can't keep the back end in check, look into a bigger front roll bar. If the front end plows, do not get a bigger front roll bar.
From this point forward, anything you do (shocks, springs, solid bushings) will be a trade off in terms of ride and livability. Tube shock conversions and camber adjustment plates start to get into very big money. See how the steps outlined above improve the handling before you spend a bunch of money.
A word on brakes. Often people improve performance in terms oaf speed without thinking about slowing the car down. Also, handling depends on quickly slowing the car down to a speed that can take the turns. As with your suspension, make sure your brakes are in top condition. If you have front disc brakes, look into high performance brake pads that resist fade and may even shorten the braking distances. Look into converting your system to high performance brake fluid that resists water absorption.