Part of me is of a mind that Wspr should be omnidirectional.  However most people on 4m use horizontal yagi antennas. There are good reasons for this which I don't need to go into here. I did try a turnstile (horizontal omnidirectional antenna) back in 2010. It was unsuccessful. However there were very few stations around and no map tab on the website to advertise my presence. Perhaps I will return to this one day.

Simple turnstile tried back in 2010.

At the moment a horizontal dipole would seem to be the minimum requirement, with a yagi the de facto default.

Currently I use a 3 element yagi.

I have one of these, a Sirio CX-4-68. It is nicely made and appears to be a J-pole. It tunes really well too.

I am ready if ever anyone decides to go vertical - HI!