There is no “best” image size. Your success doesn’t depend on which size you use, it depends on the message in your ad.
You should also consider the sites you are targeting. Most will display one or two sizes and it will also depend on whether someone is using a desktop or mobile device. You need to cover all possibilities. For instance, 728×90 has always been a favorite size for desktops and 300×250 as well. But not all sites choose to display them. Some prefer the skyscraper sizes, others the square and rectangle ones. There is of course a few mobile-specific sizes and don’t forget plain text which will be displayed to fit inside whatever size a site chooses.
Whatever size you use, it doesn’t prevent accidental clicks, especially on small screens of mobile devices. I don’t know how big this problem is however. I currently run a new campaign on display using images. One group shows 97% of impressions were on desktops, which I suspected would happen given the vertical. A text group shows the same number of clicks but 3.5x less impressions on mobile, so there may be some accidental clicking there or they simply liked the message. The tablets have less impressions but the CTR is through the roof so it appears the message is very good but more data is needed, including data by device and placements.