Life Steal and Spell Vamp don't proc based on the damage bonus source of the skill (AD versus AP), nor is it based on the damage type (physical versus magical). It's actually based on the kind of skill.
In general, Spell Vamp is the only drain effect that affects skills. All of Lee Sin's skills, despite all being AD-based physical attacks, use Spell Vamp and Spell Vamp alone. Akali is an example of a somewhat physical champion whose attack skills are all Spell Vamp-based (her innate Life Steal is to benefit her auto-attacks only). Even skills like Ashe's Volley, which applies her Frost Shot effect (but only that, the key point being as you'll read up soon), will use Spell Vamp.
Life Steal generally applies only to your auto-attack, but it also applies to skills that apply on-hit effects. For example, Blitzcrank's Power Fist deals 100% extra damage and pops the target in the air in addition to applying on-hit effects (for items like Black Cleaver). This benefits from Life Steal instead of Spell Vamp. Other examples of skills that benefit from Life Steal would be Irelia's Bladesurge, Ezreal's Mystic Shot, and Gangplank's Parrrley.
As far as I know, there is no skill which benefits from both Spell Vamp and Life Steal. It's always one or the other.
The Spell Vamp portion of the LoL Wiki and my own experience show that
[Spell Vamp] works off of activated item effects, summoner spells, and abilities, regardless of the type of damage done.
Therefore, items that give proc effects to attacks like Bloodrazor, Wit's End, Malady, Wriggles etc, will NOT grant the user health through spell vamp.
On a side note, Ezreal's Mystic Shot (Q) applies on hit effects, including but not limited to, lifesteal.
Best Answer
So I think that I'm seeing two real questions here:
The first question is a bit of an odd case, because it really depends on what you mean.
On-Hit Abilities
Some abilities, such as Gangplank's or Ezreal's Q are treated exactly like auto-attacks. These trigger on-hit items like Black Cleaver, as well as trigger Life Steal and other effects (depending on the champion).
On-Next-Hit Abilities
The second kind of attacks are "on-next-hit", which modify the champion's next attack and reset the auto-attack timer. These are abilities like Nasus' Siphoning Strike, Blitzcrank's Power Fist, and Garen's Decisive Strike. These also trigger Life Steal and not Spell Vamp.
However, to confuse things, there are also "On-Next-Hit" Abilities that trigger spell vamp, such as Poppy's Devastating Blow, and Mordekaiser's Mace of Spades.
Note that Poppy only has spell vamp in this picture. The 15 damage that is visible is from Malady's proc, which was triggered by Devastating Blow.
The only difference between the two types of abilities is that one adds a bonus to your auto-attack, and the other one replaces your auto-attack. The easiest way to test this is to use the ability against a tower. Since towers are (essentially) immune to abilities, if you use it against a tower, and it does not consume the charge of the ability, it uses spell vamp. If you do manage to deal bonus damage to the tower, it uses life steal.
Physical Damage Abilities
Finally, you have some abilities that deal physical damage, but are not auto attacks. These are things like Garen's Judgement, or Urgot's Acid Hunter. These things deal physical damage, but, because they are abilities, use Spell Vamp instead of Life Steal.
In general, any given ability onlys benefit from Life Steal or Spell Vamp, not both.
So, should you rush a Will of the Ancients? It depends entirely on what champions you have on your team.
Spell Vamp and Items
As to your second question, the answer is much simpler: Item's with on-hit damage effects, such as Wit's End, Madred's Razor (and derivatives), or Malady, never proc Spell Vamp.
Deathfire Grasp or Hextech Gunblade, items with direct activations, however, will.