League-of-legends – choose any items and have their effects stack

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.

Boots are a specific case. You can't have more than one movement buff from any kinds of boots at all.

As for other items with UNIQUE passives, as long as you don't have the exact same item, they all stack on top of each other.

Apparently, there are other exceptions as well. From the wiki:

Unique effects that do not cumulate among differents items include Movement Speed effects from boots (only the best effect applies), proc effect of Sheen, Lich Bane and Trinity Force, and the mana gained from Tear of the Goddess, Manamune and Archangel's Staff.