Optimal type of wine bottle opener? The type of opener I typical use for wine bottles is the winged lever corkscrew type:



The main problem I have with these is that they don't actually pull the cork all the way out. You have to lever out the last quarter of an inch. Also, there is the chance that you could crumble the cork into the wine.

The other main types seem to be the prong type, the hinged corkscrew, and the gas injection needle. I have not experimented with those. Theoretically the needle would seem to be best because there is no risk of crumble and it will force the cork out in one movement, assuming a big enough pumping handle, but not having actually tried one, I don't know if there are any hidden gotchas.

If we ignore cost and size as criteria, and consider only speed and convenience, what is the best type?

How do different types of wine bottle openers compare for speed and convenience (ignoring cost and size as criteria)?
Simply look at what the vast majority of waiters at restaurants use.  Speed and convenience is their top priority.  They mainly use the hinged, "waiter's corkscrew".  It is also the choice of most wine "geeks" I know.  It's what I use.  That, and an "ah so" cork puller for very old vintages/potentially damaged corks....With any corkscrew, some care has to be taken, depending on the bottle being opened.  

(While I think this answers your question, the question may be flagged as opinion based.)