Why did Varys support the plot to assassinate Daenerys Targaryen?

Question

This question may contain spoilers for season one and season five.

In the season one episode, "The Wolf and the Lion", the small council discusses the imminent threat of Viserys and Daenerys Targaryen. It is announced that both Targaryen children should be killed in order to preserve the peace in the Seven Kingdoms. The small council seem to agree that this is the right thing to do, including Varys.

My question is: Why did Varys support the assassination of the Targaryen children?

When I first saw this it made sense. Varys seeks to "serve the realm" and only wants peace. It occurred to me that he justified the decision because it would mean longer-lasting peace for the world if the Targaryens are not able to cause an uprising and ultimately war.

However, previously in the same episode, Varys meets with Illyrio Mopatis. The two discuss their already-in-action plan to restore the Targaryens to the throne. It seems to be implied that it is intended that two powerful houses, Lannister and Stark, are to fight in order to disrupt the stability of the Seven Kingdoms. Varys states that

the conflict between the Lannisters and the Starks will soon escalate into a civil war

The gameofthrones.wikia.com article goes on to state

Despite Varys's meeting with Illyrio, later at a small council meeting he seemingly supports King Robert's proposal to assassinate Daenerys Targaryen.

But it doesn't give any reason or further explanation.

Furthermore, earlier in the same episode, Varys tells Eddard Stark

the king is a fool and will soon be dead

Varys is referring to King Robert Baratheon. Varys clearly believes him to be an inadequate king.

In the season five episode, "The Wars to Come", Varys goes on further to dismiss Tommen Baratheon and Stannis Baratheon as adequate kings, describing Tommen as weak and Stannis as ruthless.

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Questions and further thoughts

1. If Varys was "pretending" to want the Targaryen children to be executed (to seem loyal), isn't that a big risk? What if the plot had succeeded and Daenarys and Viserys had been killed? Could he not have sided with Eddard Stark and said that the Targaryen children are not a threat?

2. At the time of the small council meeting

   Viserys is still alive

   Doesn't this mean that Varys supports Viserys or perhaps both Targaryen children, rather than just Daenerys? With all of Varys' wisdom and knowledge, shouldn't he know that Viserys is actually ruthless and stupid and would make a terrible king? Was it his plan to restore Viserys or was it always his plan to restore Daenarys?

3. During the meeting with Varys and Illyrio Mopatis, it is implied that they are orchestrating the plan to install Eddard as Hand of the King and establish a conflict between House Stark and House Lannister. However, we also learn that

   It is Little Finger that is really orchestrating the whole thing and that he is responsible for the death of Jon Arryn, setting in motion all events in subsequent episodes.

   Why do Varys and Illyrio Mopatis seem to take credit for this? Are they really in as much control as implied, or merely taking advantage of whatever events they are presented with?

Answer 1

Your supposition in post-script #1 is accurate: Varys appears to support the attempt to assassinate Danaerys, but secretly tries to make sure it fails. In a later episode, Jorah gets a message from Varys. In the show, I think the message merely says that he's been pardoned and can go home, but I believe we're supposed to interpret that as a coded message warning him that Dany is in danger. (In the novels this is called out a bit more clearly, as described in https://scifi.stackexchange.com/questions/37908/how-is-the-murder-attempt-consistent-with-varys-plan).

As for why he's willing to take that risk, and why he would knowingly support a terribly king of Viserys, that is probably a huge spoiler. For now, all I'll say is that there's still a lot we don't know about Varys' end game. However, given that Season 5 is largely based on A Dance With Dragons, my suspicion is that we'll probably see his plot unfold more very soon. (If you really want to know, spoiler at the end.)

In regards to you post-script question #3, I'm pretty sure if you watch the dialog between Varys and Illyrio, one of them explicitly says that the events are happening "too soon". The two of them had their own separate plot to cause war in Westeros, to pave the way for the return of the Targaryans, but Littlefinger's meddling has forced them to step up their timeline.

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If the series progresses in the same manner as the novels (which is no longer certain, especially given some of the characters that have been written out), Varys' ultimate goal is explained in this question:

(MAJOR spoiler) https://scifi.stackexchange.com/questions/63885/whats-the-deal-with-illyrio-and-varys

Ultimately, they want to bring Rhaegar's son Aegon back, whom he secretly rescued and fostered out somewhere safe. Viserys was mostly intended to be a distraction until it was safe to reveal that Aegon survived.