Okay, so Altmer, Dunmer, and Breton are probably decent choices to start. Altmer has the +50 magicka which is something that no other race can compete with, Dunmer have the innate fire resist which counters the Vampire's weakness, as do the Bretons but not as much. Apart from that, any race can really work as the skill bonuses are really a mute point. By the time you get to about Level 15 - 20 you have all your skills leveled and chosen appropriately.
To start, the Mage or Lover Stone to help boosting your Magic skills or all of them if you plan to use a lot of others, and after that it really depends on your playstyle, preference, and the bonuses. If you were to go with a Breton for example, the Lord Stone (+25% Magic Resist, +50 Armour Rating) has a good synergy, where as something like the Atronach Stone (+50 Magicka, +50% Spell Absorption, +50% Weakness to Magicka) or the Apprentice Stone (+100% Magicka Regeneration, +100% Weakness to Magicka) offer greater utility to your spellcasting, but at a cost that is fairly detrimental if unheeded.
Let's look at a Vampire for your Primary Skills, what do they get bonuses to? Stealth, and Illusion. Which help strengthen the idea of staying out of the action for as long as possible. A rule of thumb I like is one offensive skill (in this case, Conjuration), one defensive (Stealth), and optionally one utility (Illusion) that is used to assist your offensive, defensive, or both. As for secondaries, try skills that while are useful for you, don't require a lot of effort that is opposing to your character (e.g. Two Handed). You mentioned Royal Vampire Armour so we can add Light Armour as a secondary. It's a passively leveling skill that doesn't need great attention to detail. Restoration is another possible choice if you prefer to not use potions.
With enchantments, try not to fret on them in the early game, establish your character and play them until about... Level 25. Then think about what you are using a lot, having trouble with. Are you running out of Magicka, or health? Being seen too much, or don't have enough squishy meat shields between you and your enemies? In time you'll learn about the nuances of your character and how you can either boost your strengths or reinforce your weaknesses. And I'm no RP expert so I don't have any advice on that, but that doesn't mean you can't just work on it as you play. No matter what, if you enjoy it, work with it.
