What sort of bicycle helmet gives me better speed?
I think this is kind of a non-question. You want the helmet that rides the fastest? For anything "fastest", either components or kit, just look at what the professional riders are using.

This seems to imply that you either wear a regular-design lid (albeit one which is very light, very ventilated, and probably very expensive). Or, you go for a time-trial helmet.

I know some team helmets used to be made by Giro (as I bought one, Ionos springs to mind, but I'n not 100%). This was a couple of years ago, I would assume it is still the case. As for the exact model, just look at the top of the range. At the start of this year's Tour de France, a bike shop I follow on Facebook ran a competition to win a Team Sky helmet - manufactured by Kask. So there's two manufacturers to give you a start.

As regards TT helmets, when I watch time trials a lot of the riders seem to wear Specialized lids, not just the Specialized team. So they might be a good place to start looking.

I presume you realise (and accept) that for this kind of top-notch quality, you will pay.