The best call to action in display advertising is no call to action.
A link is by its nature an implicit call to action. People know they need to click on links to get to the destination of that link. People know they need to click on a display ad to get to the destination of that display ad.
The only action people can take on a display ad is a click (or a hover). Everybody who might ever click on a display ad know this. People know to take an action on something, they need to move their cursor over that thing, and click it. People behave this way by default. A link is, by default, an implicit call to action. A display ad is, by default and by context, an implicit call to action just by its very presence.
Never ever insult people with ad text like "Click here" or "Click here to begin." People already know they need to do that.
Call to actions on display ads don't necessarily mean more clicks, nor more conversions. You can test this. You should be testing this. (with multivariate tests). In my experience, I've observed that display ads without explicit calls to actions actually earn more clicks and conversions than display ads with calls to action. Of course, this could just be from the season, or for the audience, of the ads I've observed. Every audience is different. But all audiences know that to take action on something, they'll need to click it.
Use your available messaging in display ads to capture attention. Get the attention of your audience. Do not waste your limited display ad space with meaningless, even insulting calls to action. Just tell or imply to the audience what the destination of that display ad is.
Caveat: I know this is heresy for many legacy advertisers, and against the grain of many online advertising "experts". I only report this having observed that ads prove more effective following this strategy. You need to test in your own campaigns to determine if this strategy is effective for your audience.
See question on Quora