'87 MR2 Understeer

an 18mm rear swaybar will do the trick nicely to get rid of most the understeer, leave the front stock swaybar. 
 
but you will find she might get a little bit tail happy on really tight corners and in the wet especially, putting a fatter on on the front can balance the fatter rear, but will bring some understeer back into the equation.
 
wheel alignment when you have the rear bar can help keep it more stable from the oversteer tendencies. 

You should be able to get the car close to how you'd like it just with a wheel alignment. Also look at your tyres. If they're crap, you'll find that you can't lean on the front tyres enough to get the back to break loose. So with good tyres the car might be more balanced. 
 
My sw20 has ranged from ridiculous oversteer in every corner, to crap understeer in every corner (especially the tighter corners) with the only changes being made to the aligment.
 
When it was oversteering really badly, it was because I didn't have enough rear camber so the tyres were running on the shoulders and sliding everywhere. I added more neg camber at the rear and that worked too well resulting in heaps of understeer. After that, I added a small amount of toe out at the front (1mm per side), reduced the rear toe in to 0 and the car feels pretty balanced now. I still need some more camber at the back though from looking at the tyre wear. I've got an adjustable front sway bar which I can use to dial out any understeer/oversteer I might get from the alignment change.

Adrian - Tyres look ok, but like you say as soon as it comes to the nitty gritty the front loses out way sooner than the rear (exception being a steep uphill on greenhill road when wet) Ill check my alignment, and see if adjusting any camber helps around the corners, especially if I get an 18mm bar in the rear
 
Wiso - Ill have a look if any sw20's are being split and see if I can grab their sway bars, if not whiteline seems like a good route, ill put them in and then get the tyres aligned, and see how the understeer plays up and see if i need to bring in a little bit of camber to clear up the problem. 
 
Thanks guys

Interesting read guys, I'm finding my car has similar tendencies. I know my tyres are crap and alignment is up the piss, something I'm looking at remedying soon. Considering 4mm total toe in on the rear, 2mm total toe out on the front, 5-6 degrees of caster and as much camber as they can get.

MonsieurDeux
Are your tyres going to survive long with that!? lots of camber, toe in and out  im sure it will handle well though

Probably not lol! The car is mainly for weekend motorsport, won't really be doing much street time.

for tyre life he doogs is close to the money for toeing. but camber for tyre life neg1 ->neg 1.5 front and neg1.5 for rear each side. you can usually go up to neg2.5 all around. maybe neg2 on the front some have saidi

I have noticed a big difference with my '88 AW depending on how the shocks are adjusted.