As tempting as it would be to start with Gun-Fu (AGI 10), I would more likely pick the lockpicking / hacking perks first. In the early game, I don't expect combat to be too strenuous since some players are still learning about the game, so they don't want to make it too hard, and everyone will have only lowbie / early found weapons. So I don't see the need to invest in, say, Solar Powered at level 1 or 2. But I can very easily see them putting a locked safe or a computer in an early area and I hate to think I'd have to come ~back~ to it later.
Of course that depends on whether the perks make it ~easier~ to lockpick/hack or they make it ~possible~. I mean, if you can TRY to pick a lock without the lockpicking perk, and it's just harder to do so, then I might just save/reload a few times to get an idea of how hard the lockpicking mini-game is, and practice at it a bit in the process. But if you have to have the perk to even ~attempt~ the lock / computer then that would be my first choice(s).
After that, likely Black Widow or similar conversation-boosting perks. Settlement-oriented, Companion-oriented and to a degree Combat-oriented perks would be farther down the list than these "access" perks (lockpick, hack, dialog).
As for the VANS perk --- I can see where it might come in handy at times, but we haven't had anything like it in previous games and we've still managed to find out way to the quest markers without ~too~ much trouble (the New Vegas vault that was overgrown with plants was very frustrating, though, and I would have loved VANS there). So ~if~ I got that perk, it would only be after wandering aimlessly trying to find a quest location and failing constantly. And even then I might just move on to something else and try again later rather than sink a perk point into it.