Firstly I’ve got to say that your car looks fantastic with the Mazdaspeed body kit, part of which was 18" wheels so I’d stick with them.
You don’t say if it is the 2.0l sport version of the MX5. If it is it will have Bilstein dampers already.
When I bought my 2007 2.0l sport 6 years ago it was fitted a new set of Accelera tyres all round by the dealer. To put it mildly they were scary, totally unpredictable as to wether I would experience understeer or oversteer in virtually every corner, irrespective of road and weather conditions. Replacing those tyres made a huge improvement.
Next step was to fit some Eibach 30mm lowering springs, mainly for aesthetic reasons as I wasn’t keen on the huge arch gap, it’s a sports car not an off road 4x4. Didn’t notice much change in the ride quality but the handling improved with a reduction in the floaty wallowing feel round corners.
Finally for the icing on the cake I had the alignment set for fast road use by Paul Roddison in Sheffield and at last I had a car that worked with me rather than fighting me.
In conclusion I would suggest firstly making sure all the tyres are at the same pressure (29psi).
Then take a trip up to Sheffield to Roddisons and get the alignments checked over.
If its no better after that then the next step is probably a new set of tyres.
If the springs on an ND are the same as on a NC, then I have a brand new set of springs taken off my ND when it came with the sports suspension. I am happy to just let you have them if you want them (and if they are suitable - anyone?).
Hi im not sure if they would fit but can definately find out. Thank you.
The Delrin door bushes come from
robbate1@hotmail.co.uk
They are £25.00 a pair and made a big difference to my car.
They are easy to fit, just two 10mm bolts per side
If you are fitting some - put them on loose and close the door - they will then seat properly and can then be tightened…
So with all the advice from you guys i took it for 4 wheel Hawkeye alignment and balanced all 4 wheels were out quite considerably. Only drove about 2 miles back home and already a big improvement. Ive ordered the door bushings too. This will do me for now until i can afford to buy some decent 17" alloys and tyres and then get it set up for them. Thank you everyone for your input 
Pretty sure there are instructions with them but, as said, start off with them loosely fitted but not so loose that they will lose position when you open the door again. So, loose enough that the cup will centre them as you close the door but not loose enough for them to move as the door opens. Then progressively tighten while shutting and opening the door each time.
Do this with windows open or the fit of the bush in the cup may seem tighter than it actually is due to the air pressure created as you close the door on a small,
sealed cabin.
I smeared Vaseline on the bushes and cups afterwards
For a nice smooth sliding fit. 
Asked and answered, thanks for updating on the outcome 