Dragonsreach in the distance
You read about this awesome thing somewhere, and it sounded super cool. And maybe it is! You do you.
But you don't need it.
Neloth: Yes, yes. You're Dragonborn. We're all very impressed.
Unrelenting Force (Fus Ro Dah) is one of the more practical shouts when enemies get up in your face.
Unlocking the full potential of the shout will take a very long time:
To unlock shouts and learn the first word, follow the main quest line: Unbound, Before the Storm, Bleak Falls Barrow, Dragon Rising.
To learn the second word and third word, continue the main quest line: The Way of the Voice, The Horn of Jurgen Windcaller.
To gain the Dragonborn Force upgrade, travel to Solstheim and start the Dragonborn quest line: Dragonborn, The Temple of Miraak, The Fate of the Skaal, The Path of Knowledge. The upgrade is at the end of the Black Book: Epistolary Acumen.
To gain the Force Without Effort upgrade, return to Skyrim and continue the main quest line: A Blade In The Dark, Diplomatic Immunity, A Cornered Rat, Alduin's Wall, The Throat of the World. Talk to Paarthurnax to meditate on the word Fus.
Elemental Fury
Elemental Fury (Su Grah Dun) speeds things up if you insist on killing people up close.
The words are all over Skyrim:
Dragontooth Crater, northwest of Karthwasten, in the Reach.
Up on the mountainside of Shriekwind Bastion, northeast of Falkreath.
Near the Statue to Meridia, west of Solitude.
The shout only works if your weapon is unenchanted. However, if you dual-wield, only your left-hand weapon needs to be unenchanted.
Barbas is the best boy.
You can have a dog in addition to a follower, for twice the meat shields and twice the blocked doorways.
Since you probably don't want your good boy to die, get Barbas. He's invincible, because reasons.
Once you reach level 10, talk to Lod the blacksmith in Falkreath and do the Find the Dog outside Falkreath miscellaneous quest. Talk to Barbas, then follow the A Daedra's Best Friend quest and talk to the statue of Clavicus Vile. Barbas will then become your dog... until you complete the quest, so just don't.
Behold Shadowmere!
Horses can traverse slopes at ridiculously steep angles and make good archery practice targets, but they aren't much faster, and you can't pick flowers from horseback.
If you're dead-set on a horse, these are your options:
They're all the same except for looks. You only need to buy one. It'll travel with you.
Ignore these. They're just regular horses, but they wander off. Some of them are stolen, and you'll incur a 50 gold bounty each time you mount them (witnessed by the horse itself.)
Ask any barkeep about rumors to hear about Aventus Aretino in Windhelm. Talk to Aventus and follow the Dark Brotherhood quest line. Eventually, you will be granted Shadowmere. He has incredibly high health and will respawn after 10 days if killed.
Follow the Dawnguard quest line. Eventually, you will enter the Soul Cairn, where you may find Arvak's skull. Arvak can be summoned to your side (for 136 magicka) and as such is the only horse available on Solstheim, in Blackreach, in the Soul Cairn, or in the Forgotten Vale.
Finally.
You don't need Muffle.
Boots enchanted with Muffle will make it so that your armor no longer makes noise as you sneak. That is made obsolete by the Sneak perk Silence, which you should get anyway.
If you insist on adding this enchantment to your repertoire, get it when you are exactly level 11. That is when items with Muffle start showing up in shops, though it will be hard to find. If you level up further, loads more stuff starts showing up in shops, competing with Muffle and making it even harder to find.
Archmage's Quarters, College of Winterhold
For the one time in all of Skyrim that you need more than 100 Magicka--to enter the College of Winterhold--simply...
Put on the Novice Hood you found in Helgen's torture chamber in the first half hour of the game.
Drink a Potion of Fortify Magicka. (Red Mountain Flower + Tundra Cotton, if you want to brew one yourself.)
Pray at a Shrine of Julianos. There's one in the Temple of the Divines in Solitude.
Activate the Atronach Stone. It's in the volcanic tundra south of Windhelm.
If you want to experiment with magic, enchant some apparel to make spells of that school cost less, because you don't need Magicka if spells are free.
Vegetable Soup
A waste of good ingredients, except for...
Cabbage
Leek
Potato
Tomato
Since you only need 1 Stamina to make a power attack, this lets you power attack non-stop for 12 minutes straight--which would be great if archers could power attack. (Alternatively, enchant your melee weapon with Absorb Stamina for the same effect.)
If you gobble down 8 Vegetable Soups in a row and take off all your armor, you can sprint non-stop for 12 minutes.
If only these worked...
Why spend time learning skills when you could spend gold? Once your potion brewing takes off, consider some skill training (if you still need it.)
You will need to find a trainer for the skill you want to learn. A trainer can only train you up to 50, 75, or 90, depending on how good they are. After that, you're on your own. Many trainers only train people they like, so you may need to do them a favor before you even see the option to train.
You can only buy 5 points of skill training in between level-ups, meaning you need to space out your training sessions.
Training gets very expensive. If the trainer is also a merchant, you can sell them stuff to get back the gold you pay them.
1 Small Dwemer Plate Metal = 3 ingots
The world is full of dwemer metal waiting to be smelted down and turned into Dwarven Arrows (or Bows, if you don't have the Dawnguard DLC.) You just need to...
"Waste" a perk on Dwarven Smithing.
Go down a Dwemer dungeon.
Know which bits to take home.
Not all dwemer bits can be melted down. For starters, none of the items that start with Dwemer can be smelted. As a rule of thumb, if it looks like you could turn it into a shield by sticking a handle on it, it's worth taking home:
Bent Dwemer Scrap Metal
Large Dwemer Plate Metal
Small Dwemer Plate Metal
Some other bits can also be smelted down, but they're heavy and don't yield much. The rest is junk.
The Necromage skill perk
This is arguably an exploit, and as such it is fixed by the Unofficial Skyrim Patch. All that aside...
The Necromage skill perk makes your spells 25% "more effective against undead." As a hidden bonus feature, this affects potions you drink.
Get the Necromage skill perk.
Become a vampire. Congratulations, you're undead, and your Potions of Fortify Enchanting and Smithing are now 25% more effective.
Continue the Loop of Power.
Optionally, get your vampirism cured.
Enchant gear to make Restoration free.
Find some enemies.
Let them whale on you while you double-cast Healing Hands. It should "only" take you half an hour to get Restoration to 70. (Take off some armor if you're too strong for your own good.)
Find a vampire. You could try one of these spots:
Haemar's Shame, east of Helgen, south of the Throat of the World.
Movarth's Lair, northeast of Morthal.
Shriekwind Bastion, north of Falkreath.
There's no biting involved. Let the vampire use Vampiric Drain on you (the red beam) until you contract Sanguinare Vampiris.
Don't cure any diseases for three days (don't pray at shrines!) to let the disease develop into Vampirism.
You're not the sparkle-in-the-sun type of vampire. Vampirism has a bunch of stages in which the sun becomes increasingly annoying (and, if you don't have the Dawnguard DLC, people will eventually attack you on sight)... unless you drink blood. It's quite the hassle. Don't hesitate to kick the habit once you get your Loop of Power done.
Talk to Falion in Morthal. He'll set you straight.