Aspects
Aspects are the core of your character in Spirit of the Century. The are colorful descriptors that let you do extraordinary things and also get you into trouble, which earns you Fate Points. And you want Fate Points. So the best Aspects are Aspects that will be descriptive, interesting, useful at times, and will also get you in trouble at times. They don't all have to be that good - some can just be trouble (Raging Alcoholic) or can just be advantages (Legendary Elven Accuracy). Its up to you. But if you have none that are trouble, you won't get nearly as many Fate Points, and that means you won't get to use those advantageous Aspects nearly as often.
Race or Racial ability: Dwarven Stonecunning, Luck of the Halfling, Warforged Don't Breathe, "I am Most Certainly Not a Changeling", "My! What Big Claws You Have",
Class or class ability: Faith in the Silver Flame, Monastic Training, Animal Companion, Cleave!, Lay on Hands, Extreme! Explorer, Eldeen Ranger, "I'm an Inquisitive Sort of Girl", "I'm the Warforged Juggernaut, Bitch!", Secrets of Elemental Binding, Servitor of the Blood of Vol, Exorcist of the Silver Flame
Dragonmarked House: Mark of Detection, Mark of Finding, Mark of Handling, Mark of Healing, Mark of Hospitality, Mark of Making, Mark of Passage, Mark of Scribing, Mark of Sentinel, Mark of Shadow, Mark of Storm, Mark of Warding, Dragonmark Heir (requires Mark Aspect)
Dragonmark Aspects will allow you to gain the magical benefit that is basically the equivalent of a couple related spells of lower power. You also gain the social connections that the Mark implies - marked members of Dragonmarked Houses get priviliges because of their birthright. So it isn't as powerful as, say, Spellcraft with the Necromancy Stunt, and it isn't as influential as other Aspects might be socially, but its a very strong hybrid, and will probably be useful with Fate Points pretty often in Eberron.
Magic item: Boots of Striding and Springing, "Look at My Rod of Wonders", Clunky Magical Armor, The Sword of my Fathers, Bag of Holding
Ally: I Know a Guy Who Knows a Guy,
Relationship to the world: "I Serve the Brelish Crown", Dread Lord of Karrnath, Blooded Elf of Valenar, Gatekeeper Initiate, Member of the Wayfinder Foundation, Fellow of Morgrave University, "What Emerald Claw Tatoo?"
Personality/RP: Fly off the Handle, "Oh, is that My Blood?", Don't Ruin it by Thinking, Barbarian Rage!
Some Character Creation Suggestions
Its a good idea to include at least one skill that you can use in combat. In pulp, fights come fast and furious. With SotC they aren't deadly that often, but they do carry consequences (some are listed below). Athletics is used to dodge attacks, Fists and Weaponry are used to block and parry attacks, Spellcraft and Religion and Art with their connected Aspects are obviously useful, Bows is an obvious choice as well, and so on.
You can also try to use social skills to defend yourself - though this isn't a sure way to avoid getting your ass kicked, it might save you. Deceit, Intimidation and Leadership might all be useful in a fight. Endurance and Resolve will also come up often against things you don't get a chance to try to block or avoid.
You might want to think of our character's approximate "class". The top one should be what your "class" and character do best. What's their core competency, the thing you want to use a lot during the course of the game? Put that there.
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And that's what I think is useful to copy - most of the rest of what I had was taken directly from the book and pretty obvious.
For me, the key points are the changes in the Skill list and how I handled Stunts to encapsulate Arcane and Divine magic for caster types, including some of the musical abilities of Bards, and the unique Dragonmarks. The stuff about Aspects and so on is pretty obvious, really - just something you need to work out.
I found that SotC was well-suited to Eberron (which one would expect) - it definitely broke away from that D&D "feel", but you can keep the feel in a limited way if you want to by limiting the choices you make with the system.
Obviously, if you really want that D&D "feel", then, you know, play D&D.