In terms of sign type and qualities:

The Sun and Mars are more Cardinal or active and likely to lead and to dominate.

The Moon and Venus are usually more fixed or passive, preferring to yield or to endure.

Mercury and Jupiter are more Mutable or adaptable, liking change and development especially at the level of concept and idea.

Saturn by itself tends to be fixed, tied to inertia, but its effects on other planets is to weaken them and render them mutable. The lunar nodes, Rahu and Ketu, also function as disruptive or mutable forces, unless well placed in which case they strengthen the qualities of the planets and signs they are associated with.

For instance Sun in mutable sign Gemini will give mutability to will and character because of sign type, though Sun is Cardinal type as mentioned earlier.

A fixed sign Mars in Scorpio will give fixed energy and purpose, though Mars is Cardinal type as mentioned earlier.

Each planet is also associated with one of the 4 elements as its dominant characteristic.

Sun is associated with Fire element.
Moon is associated with Water element.
Mars is associated with Fire element.
Mercury is associated with Earth element.
Jupiter is associated with Fire element
Venus is associated with Air element
Saturn is associated with Air element.

No elements are associated with the nodes, they take on the elements of the sign where they are located or the planets with which they are associated in a particular sign or with the ruling planet of the sign they are located.

In fact the planet rulership of a particular sign is basically determined by the sign type and elements of each sign and each planet, as discussed above.

First we shall analyze the rational behind the planet rulership of each sign based on the considerations discussed above.

Aries (Cardinal & Fire) ruled by Mars (Cardinal & Fire)

Taurus (Fixed & Earth) ruled by Venus (Fixed & Air)

Gemini (Mutable & Air) ruled by Mercury (Mutable & Air)

Cancer (Cardinal & Water) ruled by Moon (Fixed & Water)

Leo (Fixed & Fire) ruled by Sun (Cardinal & Fire)

Virgo (Mutable & Earth) ruled by Mercury (Mutable & Earth)

Libra (Cardinal & Air) ruled by Venus (Fixed & Air)

Scorpio (Fixed &Water) ruled by Mars (Cardinal & Fire)

Sagittarius (Mutable & Fire) ruled by Jupiter (Mutable & Fire)

Capricorn (Cardinal & Earth) ruled by Saturn (Fixed & Air)

Aquarius (Fixed & Air) ruled by Saturn (Fixed & Air)

Pisces (Mutable & Water) ruled by Jupiter (Mutable & Fire)

You will observe the rulership of Aries, Virgo, Sagittarius and Aquarius matches perfectly the rational of types and elements of sign and planets.