star wars - Why was a clone army needed to eradicate the Jedi Order?

Let's look at the Attack of the Clones script for answers

LAMA SU:
We modified their genetic
structure to make them less
independent than the original
host. As a result they are
totally obedient, taking any order
without question.

(snip)

OBI-WAN:
You mentioned growth
acceleration...

LAMA SU:
Oh yes, it's essential.
Otherwise, a mature clone would
take a lifetime to grow. Now, we
can do it in half the time. Those
items you saw on the parade ground
were started ten years ago, when
Sido-dyas first placed the order,
and they're already mature...

(snip)

LAMA SU
They're immensely superior to
droids, capable of independent
thought and action.

Why did Palpatine order a Clone Army for his grand plan?

Palpatine wanted an army that was intelligent, effective, and obedient. The clone army fits all of these criteria - and could be created in secret and revealed exactly when he was ready to use them.

Couldn't any other army do? Definitely, any army would follow Order 66.

A droid army is the only other type of army that would be 100% obedient. The clone troopers spend years fighting alongside the Jedi. The average soldier is not going to turn and kill their friends without hesitation just because their commanding officers/commander in chief tells them to. The clones were genetically modified to obey any order, and no order could supercede the Chancellor's.

Also, there was a possibility that Jedi Council and Senate wouldn't accept that Clone Army.

This is a possibility - but Palpatine engineered events so that the Jedi would discover the Separatist Droid Army and the Clone Army at the same time. With no other standing army to battle the Separatists, a clone army genetically bred to be loyal to the Republic is going to be awfully hard for them to turn down.

After coming into power, couldn't he order for a grand army creation or simply officially order a clone army?

He could order the creation of a non-clone army, but would have to deal with issues of loyalty and quality. He could order a new clone army, but as Lama Su explains, it takes time for them to be grown. The clone army was commissioned 10 years ago, and is only now ready. That's far too long if they are to fight the Separatists.