Hiya. I've probably come to this a little late, but here goes...

The easiest way to keep your old Startpage/Speed Dial settings, etc (between PCs at least), is to copy the entire Opera Stable folder from one PC to another (it's usu less than 20MB so it's not massive), you can find it here:

%appdata%/Roaming/Opera Software/Opera Stable

If you're running Opera at the time, you'll get a couple of 'cannot copy' or 'file in use' errors - this is just the files and tabs that are currently open.

For those using Windows 10, you can find the %appdata% folder by literally just putting "%appdata%" in the Start/Search box...

Hope this helps. If you're feeling more daring, you can look at the files using Notepad, which'll at least tell you what you have and haven't got in each one.