To jump into the fray here... This is a TLDR, you've been warned... I would like to see us go back to the DAO system of who equips what. I am making an assumption that we are keeping the Warrior/Rogue/Mage trifecta and that there will be only two specializations to choose from per class. I'm making this assumption on the basis of an early Q&A about DA3 that happened last year. Fans asked if their class might elicit different responses from npc's, ala if you are an unabashed bloodmage as opposed to being a Templar of the Order. I make an assumption based on some events and interviews that have happened with the DA creators. My opinions are my own, and reading this thread I realize that some people want to unbind all weapons. I'm of the opinion that this is very hard to do with the current 3 class system where weapon is tied to talent for the purpose of cross-class combination attacks in many cases. I must admit that I do not want to see such combination attacks go away. You could get around this by making all talent trees for all classes interchangeable, but I don't see this happening. I lament the loss of my Archer-Warrior who could wear heavy armor and still have some degree of mobility, I really do.
What follows from this is that you have weapon availability work via specialization. In fact, it wouldn't surprise me if the new origin system determines your specialization or if you choose your class and specialization and origin as separate things from the character creation screens.
For mages, it's easy to say that we're likely to see the Blood Mage and Spirit Healer return. There are gameplay reasons as well as lore reasons for this to be so. We're having a Mage-Templar war, so unless there's a big Elvehen connection that's yet to be revealed, I think we won't be seeing warrior magi. Unfortunately, DA2 points to less segregation of lore and gameplay. But I would rather see less segregation of lore and gameplay if my decision to play a Blood Mage will impact how followers and other npc's respond to me.
Warrior is harder to peg, but the presence of Reavers in expanded content like the live action DA series would point to Reaver remaining an advanced class. The whole dragon blood thing and the connection to blood magic makes it harder to believe that we'd see Reaver cut in favor of a Berserker. I can't see a DA3 where there isn't a Warrior Templar specialization because of the Mage-Templar war. I see Berserker being dropped because of its portrayal as a dwarven thing and complete absence of a berserker type follower from DA:2. Maybe Ogren returns and I'm wrong, but this is my educated guess. Or maybe we get Ogren or another follower to carry the berserker mantle while we don't get the specialization.
Rogues get messy. Since we're in Orlais, I want to say that the Bard specialization may make a return with our Orlesian Bard being more than just a minstrel. This way, we get our bow-wielding, sniper-assassin bard. The other option I'm less certain of, because I don't know whether the super-sneaky, double-dagger assasin is more popular in the community than the in-your-face duelist.
But by these archetypes alone you see how we fall into the tropes of what these guys should be wielding. I never understood why a Blood Mage in DA2 couldn't ditch his or her staff in favor of the trademark dagger. Blood Magic animations in DA2 looked funky because of the staff usage, imho. I could buy a Blood Mage wielding any 1 handed weapon as long as the bloodletting animation was convincing. Too, I could go for the staff being ornamental and hanging from your back while we got to equip a 1-hand bladed weapon for Blood Magic purposes.
I see your Spirit Mage being bound to staves, demonstrating their use of more "traditional" and "safer" magics. By the same token, we might make the assumption that all mages have gone rogue, and thus maybe all mages have gotten some one-handed weapon training.
I would like to see Templar Warrior having no weapon restriction at all seeing as how there were Archer templar and other lightly armored templar in DA2. The shield with the templar coat of arms is fairly iconic, though, especially after Aveline in DA2 and the plot point that became. I loved putting Alistair in Templar Plate even when better gear was available just for the look. Tanking in DA2 was possible without the sword and board tree, but you certainly lost some tools. The magic-nullifying, defense-oriented templar is mechanically easier to implement and more iconic by lore. Other types of templars are seen all over the place in DA2, so lore is still on your side if you want an archer templar or a fast templar. But all the "important" templars were sword and board. This also follows the differentiation of the Mage, making the Templar the more trustworthy archetype while the reaver, described below, would put npc's on their guard by his mere presence.
I'd like to see the reaver able to equip anything that is an effective melee weapon. This includes dual wielding. If dual wielding for warriors carried an armor penalty, I wouldn't weep.
Orlesian Bard - I'd like to see an amalgamation of the DAO bard tree and the DA2 Assasin tree here, with the ability to equip a bow or dual wield any two single-handed weapons. Depending on the npc's knowledge of Orlesian Bards, responses of npc's could range from passing off your character as a minstrel to suspecting that your actions may be motivated by one of Orlais's many aristocrats.
The Other Rogue Spec - The pro of going the Duelist route is that you could justify a tanky rogue with a shield or a 2h rogue because the duelist, by virtue of being the non-sneaky rogue, kind of breaks the "rogue mold" by definition. This is my preference, but others prefer the Shadow who does everything based on stealth and illusions, and sneaking would realisticly require lighter weapons (daggers, bow).
I'm expecting a lot of people to just say no to this idea because either they want full customization of character or because they want the talent system to work in a different way. This is how I think weapons should work depending on your specialization, assuming your specialization will effect how npc's react to you, and assuming that there is a certain degree of real world logic in why some specializations shouldn't be able to use certain kinds of weapons. make of it what you will.