No, you don't get to pick. You get a list of 4 things you must accomplish or no daily reward.
Let's say you pick PVE and WvW. Then you have to complete all the 4 dailies selected FOR YOU BY ANET, not "by you" as before in the previous dailies system.
I did not like what came up the first day for my account. But when I went to my second account, and picked just PVE, the choices FOR ME BY ANET were completely different from the previous account (the 2PVE ones from the previous account were not there) and just as annoying.
One of the dailies was to complete a Kryptis Bounty Event, with no explanation of where to find it, on DAY 1 of the expansion, and nothing in the wiki, of course, because we don't want spoilers. That was a crappy choice to force on a person on day one. I asked around and no one had an answer.
I think the vault idea is a good one, but the implementation is rather unfinished and as currently working, diminishes the game, and discourages players (as all the negative comments reflect).
And the kicker is that if you uncheck one of the three types, it doesn't take effect until the next reset. And if you uncheck WvW, then tomorrow you might lose out on a daily that you could accomplish, while picking up PVE ones that you cannot.
Please give us back choices, and eliminate the "locked out until tomorrow" checkboxes.