Misfire on Startup Problem

Hi MR2 Forums, first post here. :)
 
I recently came into possession of a 1990 MR2 SW20, with an NA 3S-GE (because Australian P's), with around 175,000km on it. It seems to be a half decent car considering age and mileage, and I'm hoping that it will be one that I can keep for a while and gradually restore to a nicer condition than it's in now. Main reason I got it was to replace a dying AE82 that'll most likely be off the road for a while until I get the 4A-GE blue top rebuilt, but that's another story entirely...
 
I wasn't too sure whether to post this in the engine or ignition section, since I'm not entirely sure where the issue lies... I apologise if I got it wrong.
 
Anyway, it's been having a little bit of trouble starting, particularly on a cold start after it's been left for a while. If I give it turn the key and let it start, RPM will jump all around from 400 to 1000, it'll run rough, cough and splutter for about 5 seconds with a flashing engine light or so before kicking into life and idling normally. I gave it a start yesterday to move it so I could replace a seized handbrake cable after it had been sitting for the weekend, and it was more like a good ten seconds. It only really does it to this extent on a cold start after it's been left for a day at work or something like that. Strangely enough, it rarely gives me that much trouble in the morning. A warm start is like any other car, except pretty much every time you can hear a cylinder miss at least once before it idles properly. Driving is normal, the engine sounds regular and even both at idle and on the road.
 
I guess my question is, where do I start? Do I have a cylinder that's close to death with absolutely crap compression, essentially a lemon engine? Or is it something to do with the ignition/electrics side of things?
 
Oh yeah... a couple more things, unrelated. Any suggestions for a replacement exhaust? I was looking at a Fujitsubo Legalis R from RHD Japan, but they're mad expensive and getting it here would cost half the price of the exhaust itself. As well as that, what oil do you guys recommend, considering its mileage?
 
Any help is appreciated, this is driving me insane.
 
Thanks,
 
-J

As dylmrt has said above. Do all the cheap bits and pieces first as it could be an easy fix. Then look into things like timing etc. I had the same symptoms as you do on a rebuilt 3sge. For me it turned out to be an incorrectly bled coolant system. 
 
For oil i use to run 10w-40 Magnatec and am now running 10w-60 Edge. As long as you go with a name brand with the correct oil viscosity for the engine you cant go wrong. 
 
As for the exhaust. If your interested in just a cat back system and are in Sydney. I have one that i might sell. PM me if you're interested.