Apologies for being late to the discussion, bu please bear with me while I share my thoughts on the introduction.
My preference would be for the film to start with the Bilbo's encounter with Gandalf, followed by the opening credits and then leading into the arrival of the Dwarves.
However, I recognise that it is fairly standard nowadays for films to open with an 'action' scene and that it is therefore a part of audience expectation (I blame the James Bond films
). If this convention is followed, Smaug's attack on the Lonely Mountain is a possibility (with Smaug never fully shown), although I tend to agree that this is probably best left for the Dwarves to tell in flashback. I don't think that Gollum is a sufficiently central character in this tale for his loss of the Ring to form the opening scene (nor, indeed, is there enough 'meat' to it, I think, to fulfil this role).
One further possibility is to have Gandalf's covert entry into Dol Guldur and meeting with Thrain in Sauron's dungeons as the opening scene. It is central to the plot, as it is the means by which Ganadalf obtains the Map and the Key. And, while it is not 'action packed', it would be sufficiently tense and have enough action to make a good opening scene. Gandalf's identity could be concealed until he reaches Thrain and draws back his hood, adding some mystery to the scene. If there was time, the scene could then cut to Bree many years later and Gandalf's meeting with Thorin, culminating in Gandalf agreeing to find him a burglar.
Cut to opening credits, leading into a blissfully unaware Bilbo smoking his pipe (would that be allowed?) outside Bag End and Gandalf's arrival.