Dropping the ride height back to the chrome bumper ride height, or thereabouts, is a popular way to improve the handling. There are two main approaches and if you go the much easier route of lowered springs you should use significantly upgraded front springs and a heavier/thicker front antisway bar to limit any bumpsteer. This works for me. I'm using a 7/8" front antiswaybar and my front springs are about 30% harder than standard, which does not noticeably effect ride comfort. The rear springs should be kept soft and the antisway bar removed as at that lower ride height it is more of a minus than a plus. You should make sure that you have at least 2.5" of free travel below the rear rubber bump stop, at ride height, to prevent premature contact and snap over steer in corners. If necessary, cut a bit off the rubber, easy.
Moss sell a really neat adjustable front antiswaybar that adjusts from 3/4" to 7/8" , the two most popular upgrade sizes. You would be very lucky to pick the right antisway bar, first go (it took me two attempts) So irrespective of dropping the ride height this antisway bar is a good move.
The other more difficult, and technically better, approach to lowering, is to fit a chrome bumper front crossmemeber. There are difficulties and expense in doing this wrt the steering, I'll leave this for others who have done it to explain. With a bit of luck they will post a photo or two.
Front Shockers-Peter at world wide shockers sells adjustable armstrongs, better than factory original. I'm going to get a set at some stage.
Rear shockers-there are various kits to change to tubular. Some brands have a reputation for being much too hard (eg spax). The GAZ adjustables (32 settings)look good. I've got a set in the cupboard. Currently I'm using British automotives KYB's. http://www.mgbmga.com/ (the technical section is well worth a read through).
Others may disagree, but I feel that putting tubular shocks on the front just introduces another linkage. You lose what you gain. On the rear is OK, it's a more direct attachment, direct to axle.
POWER
Super charging is becoming popular. You can buy Off the shelf kits for this from Moss.
http://www.mossmotors.com/Shop/ViewProducts.aspx?PlateIndexID=37878
or these guys if you you want more power and are prepared to rebuild the motor
http://www.hi-flow.com/
Of course a supercharger is never going to compete with the tremendous torque and easy drivability, of a V8. The rubber bumper cars (yours) have identical engine compartments, bulkheads, engine mounts, steering and radiator cores, to the mg V8 that was produced in the mid 70's. The engine that the factory used was the Buick derived alloy Rover V8. Actually about 50lbs lighter than the 4 cylinder 1800. This same engine was continued in the Rovers and Range rovers until very recently although the more recent engines are much more powerful and economical (efi) than in 1975.
So you can put a relatively Modern Rover motor (AKA MGB V8 motor) in your MGB with off the shelf engine brackets etc without in any way adversely effecting its originality or value. Quite the reverse as per the value. The diff' back axle is well up to handling the power although you should put anti tramp bars on, which is not a big deal.
Here are a range of V8 conversions. The local parlance calls it "turning to the dark side of the force" Turn young Skywalker...turrn..
http://www.britishv8.org/Photos-MG-Conversions.htm
scroll down a bit.
and http://www.mgcars.org.uk/v8_conversions/rogv8.html
