I mainly favour a sword n board warrior, especially if I have a strong 'fire n forget' school of magic on switch (illusion/conjuration). Starting combat by quickly calling a minion or firing off a frenzy spell before wading in with good defense just feels nice!
I can never settle on one playstyle for long though...
I think my least favourite is dual weilding.
I've played most of them, but the one I keep coming back to is the sword-and-board playstyle. One of my current characters is a Khajiit warrior that uses heavy armor, a shield and a war axe and utilizes the steed stone and sneak. Also chose to disregard archery for this particular character as well, as he would become more-or-less a heavy armor stealth archer, and I don't want that.
Although I do enjoy playing both spellsword style as well as using two-handed weapons.
Definitely prefer battlemages and spellswords. My favorite characters have all been battlemages; the Sorceror, the Khulari, my current character (who I may post if anyone wants to help), Obsidian Sentinel, Maormer, etc. I just love both destruction and swords, so it's natural for me love the hybrids
I actually have a rather tactical approach to Skyrim. I will sneak, then use Throw Voice to move a single enemy near me, then silently take them out with a bow or dagger. Then I will do the same to the others nearby.
For bigger enemies, I use a bow that I call "Confusion" that has Fear and a Chaos enchant on it. Then they run as they take damage.
For Dragons, there isn't really much of a Tactical Method to taking them out. If possible, I will use a bow from cover, that way they can't attack me, but I can attack them. If no cover is available, I "go loud". I will simply run at them with two enchanted daggers (one with Lightning Damage and Frost Damage, the other with Chaos and Fiery Soul Trap [yes, I know it doesn't work on Dragons]).
This usually gives me a very fun playthrough, and allows my DiD characters to survive.