For starters, I hope the weapon types that were in Morrowind but not in Oblivion, primarily spears, to return in future games. Aside from that, it would also be nice to see a little more variety in the categories that are present in the game. In future games, I want a lot more variety in weapons to choose from, as this would allow for more room for customization.
It's hard to go into specifics on weapon animations as I'm sure that animations will be redone, but first, the animations need to be good, obviously. They don't necessarily have to be extremely elaborate, but they should feel natural and fluid,. Bethesda's animations are often not the best in games available at the time, I nonetheless hope for improvements in future games, however. I'd also like to see a little more variety in weapon animations depending on the type of weapon, you wouldn't use a dagger in the same way you would a longsword, so they should not use the same animations, Bethesda should adress the basics before worrying about the more advanced details.
Combat animations will always suffer a bit in TES due to agility stats, similar to run speed. Rather than running/attacking at a speed that "feels right", as you would in a dedicated action game, you often have a chance of the animation feeling akwardly too slow or too fast.
That's not an excuse for poorly done animations, while the animations may not be able to properly adapt to changes in rate at which one moves and attacks (though I'm pretty sure that in earlier games, no character attribute affected attack speed, only the properties of the weapon did, of course, this could be changed in future games.) but that doesn't mean the animations themselves can't be good. In Bethesda's past games, the animations themselves have often not been all that great, just look at Morrowind, over the years, modders have done a lot to make the game look much better than it originally was, not only are there lots of model and texture replacers, but programs like MGE also allow things that could never be accomplished just by replacing a texture or model, and modders are still creating new mods like this. But after all this time, they still haven't done that much to improve the original animations, so while Better Bodies and high quality faces and such may look characters look good in screenshots, as soon as you see them move, you know this is still the same game that was released years ago.