2000 is enough for any province without fortification. It will take around 1 month game time. There is attrition, meaning that your force may lose men. Since 1000 is the minimum needed, 1000 men could easily become 999, so 2000 avoids this potential problem.
If there is fortification, things are completely different. First of all, 2000 is never enough. How many men you need depends on the fortification level and ranges from 3000 to around 20k. (Again, bring a few more because of attrition). Adding more troops beyond the minimum is useless and usually bad because of attrition (cannons are an exception).
In addition, fortified provinces are not taken over within 1 month usually. You need to win a dice roll, of which you have around 1 per month. The outcome of the dice depends on many factors. You can see the chance to win the siege as a percentage. Some of them are:
- the level of the fortification (a small fort has a small malus while a large star fort has a very high malus)
- the number of cannons in your army (more is better, but there is a limit)
- the siege ability of the leader of your army, if present (more is better)
- access to the sea, modified by blockade of this access
- a few other things
- a timer, that increases over time and after a long time gives an extremely high bonus
The time increases faster the higher the sum of bonuses minus maluses is, you should always try to provide full force instead of simply waiting it out with minimum forces.
For your planning, if the percentage is x%, you will probably win the siege within 100/x turns. For instance, with 20% chance it will probably take 100/20 - 5 turns. 1 turn is around 1 month, the exact span depends on many things.
If you need to reduce your available manpower very quickly(*), you can also assault the castle under certain conditions. For that you need a lot of men. You will lose a ridiculous number of men (something like losing 17k men against a defending garrison of 1200 is not unusual). If either the morale bar or the number of (only foot, not horse) men of one faction become zero, the battle is over.
(*) That was a joke. Do not do this.