'89 Volvo 340 1.4 variomatic rough start

Hello,

This car never did anything like this before... I have to play a
couple of minutes with it before it would start. Not just cold start,
sometimes even when warm!
The oil is new, the air filter is still ok, the sparks are also look
ok, they're also relatively new... what should I check next?
I also cleaned the carb not so long ago.
When it finally starts, it also emits a LOT of smoke (normal, blue-
purpleish colour, as for a too rich mixture, but it is REALLY a lot
of smoke...), gives a hell of a sound, but when the engine gets to
the working temp, it runs like a dream: fine idle, very low noise, no
vibration.
Does it make any difference, if I start it Park or Neutral? What's
the difference anyway?

So is there anything to be checked or to be set?

(Actually, it's my girlfriend's car, I am relatively new to it,
normally I maintain my classic SAAB 900, but that's totally
different from this Renault engine :( )

Some more questions:
-What's the life span of the drive belts?
-What should I look for, as a weak point in the future?

Thanks in advance, please help!
b.m.

I don't know these particular symptoms BUT:

Park or Neutral? You can start in either and the clutch won't engage until about 3000 rpm in these because the clutch servo is energised.
But don't rev the engine in park as it can damage the clutch.
So I start mine in neutral.

Mine has a bit of a procedure to cold start:
1. Pull the choke all the way out.
2. Pump the accelerator 3 times
3. Start
4. It runs for several seconds and stops if the outside temp is below 8 degrees.
5. Do it all again until engine runs.
This procedure has never failed to start the car but it can take only one attempt in warm weather and three in cold weather.

These engines are sensitive to inlet air temperature and it is worth checking that the air temp thermostat on the inlet to the air cleaner both works and is connected to both cold air and the box on the exhaust manifold.

Also I thought grey smoke was rich mixture and blue smoke was burning oil? But this engine does not burn oil (in my experience).

Hope this is some help.