Let's look at the historical characters of this period:
Spain:

Phlip III reigned in Spain, Portugal, Naples and Sicily in 1598-1621

Philip IV, his son succeeded him.
Francisco Gmez de Sandoval y Rojas, Duke of Lerma was both kings'
Valido (Chief
Minister), until he was substituted in 1625 by Gaspar de Guzmn,
Count-Duke of Olivares, a honest and hard-wroking but limited
statesman.
France:

Henri III of Navarre and IV of France, originally a Huguenot but converted to Catholicism in order to inherit France (
Paris is well worth a mass) was a very popular and tolerant monarch.
In 1610, his son Louis XIII (Louis I of Navarre) inherited both
thrones. He revoked the rights and privileges granted to the Huguenots
by his father.

His Chief Minister since 1616 was Armand Jean du Plessis, Cardinal Richelieu.
Ottoman Empire:

Mehmet III ruled the Ottoman Empire until 1603.

Ahmed I, his son, succeeded him until 1617.
Mustafa I reigned briefly in 1617-18 and later from 1622 to 1623. He
was mentally retarded or at least psychologically ill. He was
succesively displaced by:

Osman II (1618-22)

... and his brother Murad IV (1622-40)
Austria - Holy Roman Empire:

Rudolph II, Holy Roman Emperor, King of Bohemia and Hungary, Arhchduke of Austria (until 1612)

His brother Mathias succeede him until 1619.

More famous is Ferdinand II (1619-37), whose interventions in Bohemia caused the Thirty Years' War.
England:

Elizabeth I, the Virgin Queen, ruled England and Ireland until her death in 1603.

James I Stuart inherited her. He was initially King of Scotland (James VI). He died in 1625, leaving the kingdom to Charles I.
Poland:


Sigismund III of Poland, ruled this country from 1587 to 1632. Briefly
also King of Sweden, he tried to regain his rights to that throne and
unify both crowns.
Russia:
At the start of the Century, Russia was inmersed in the
Time of Troubles (1598-1613), in which several tsars ruled for short periods in the midst of civil wars and conspirations.

Boris Godunov, born a simple boyar (low nobility), ruled until 1605,
when he was briefly replaced by his son Feodor II, who was assasinated
in a coup.

He was (also briefly) replaced by the first False Dimitry, an imposter, supported by Poland.

Vasili IV, a descendant of Novgorodian princes, succeded him in the period 1606-10.
After a troubled interregnum of three years, finally...

Mikhail I Feodorovich Romanov ruled Russia until 1645
Sweden:

Charles IX, ruled first as regent and later as king, from 1599 to 1611

Gustav II Adolf (Gustavus Adolphus),
the Lion of the North, son of the former.
Denmark:

Christian IV ruled Denmark from 1588 to 1648.