I have a 2006 Suzuki Grand Vitara with a manual gear box. When I start the car in the morning it tends to shake a bit, especially if I touch the accelerator. Just after starting, I can change up through the gears up to 3rd gear without touching the accelerator. After a while when it warms up, it is fine.
The shaking could be due to lax maintenance.
Is the vehicle overdue for items like spark plugs?
Is the Check Engine Light lit up?
When you say “I can change up through the gears up to 3rd gear without touching the accelerator”, I assume you mean that the engine is racing. If so, how many RPMs is it turning at before the engine warms-up fully?
You might want to clean the Idle Air Control, or perhaps you may need to replace it.
The Mass Airflow sensor is something else to look at.
Has the induction system ever been cleaned?
The throttle body may be in need of cleaning.