I was previously playing a battle mage focused in heavy armor, destruction and restoration. I now want to start another character. I don't want to be a mage of any sort, I either want to be:

2h melee.
Dual-wield melee.
Sword/shield melee.
Stealth melee.
Stealth archer.

Which of those 5 would you say is the most fun? :celebrate:

How about a non-stealth archer?

Conjure up an atronach
Hire a Merc
Buy a Wardog
Summon a bow
Brew poison
Hunt the wilds of Skyrim

Hm I could, though for some reason stealth archer sounds more appealing (I thought Karliah was pretty cool).

Stealth archer, but a mystic one, using conjured bows, and if spotted summoning a tank.

I love 2h, barbarian style, I say you create a archer that subs in sword & board/dual. Try 'em out and see what you think. If you want a specific type though, 2h, the glass 2h axe/sword look awesome. So do the steel great sword, the Ebony axe and the Daedric hammer

Have had the most fun with my barbarian/ranger thing. Light armor, 2handed, archery, sneak, smithing and restoration.
Start shooting things from stealth with my bow and then mop up with a big ass sword,
Stamina regen from restoration is great and a point or two in alteration beacuse oakflesh is friggin expensive when you put almost all your points in health and stamina.
Really fond of 2handed weapons, big hits with blocking and bashing make them fun to play with.

I want to try a two-handed character that uses greatswords, but I always seem to find myself leaning back towards sword and shield fighting.

How about a jack of all trades? Do a bit of everything.

I really enjoyed my stealth/illusion khajit, got a little OP around level 16 though. Right now I'm doing a more classical paladin type, heavy armor, restoration, etc. Also very fun so far!

I've always been the stealth/theif/assassin/ranger type. Basically, killing everything before they know I'm there, rarely getting hit, etc.

But I'm having a blast with my 2H heavy warrior build right now. It's just pure fun.

The stealth archer can be quite a bit of fun, but it can easily become too easy if you do too much crafting.

Another option would be a character that only uses daedric artifacts (once obtained):

I'm having a lot of fun with a heavy armor stealth mage alchemist. Raining fireballs down on people is awesome, as is casting a muffle spell, then daggering my way through a dungeon chugging invisibility potions. The only thing that really lags is straight up combat - fireball does good damage, but it's AOE so I can't use it most of the time (this isn't Dragon Age, there aren't many opportunities to brutalize crowds from a safe distance) - and the firebolt and lightning bolt spells really lack punch, Jordis ends up getting most of the kills. Maybe things will get a bit better once I get incinerate and wall of fire. Playing as a mage is making me a lot more excited for the CK, there's some real potential.

It such a subjective question. It really does depend on what you like, and in some ways, what you're best at in game.

I approached it this way with my first character... I acted like he wasn't an expert in anything. So he just did whatever seemed right at that moment, whether it was swinging a sword or putting on armor that looked cool or shooting off a spell or picking a lock. Whatever came along, I gave it a go. It wasn't too long until I had patterns of the way I liked to play, or ways I was best at playing, and found myself naturally leveling certain things up. My first character eventually was a sneak archer in light armor who meleed with a sword in one hand and shot off spells with the other. It worked out well, and I had alot of fun with him, and learned what I liked to do in game and what I didn't. After about 40 levels, I started a new character to focus on things I hadn't done with the first- a melee warrior with a sword and shield. And I love playing him as well. So I don't think there really is a "right" answer. Not sure if that helps any at all.