the miss consception of spell vamp and life steal is that they believe that its all about damage type, but its not, its damage source. key word is source.
if your damage is coming from auto attack or an ability that will proc on hit effects (which is considered an auto attack in the game's sense) you are applying life steal
if your damage is coming from an ability of your own, then it is going to proc spell vamp, simple as that, item's damage do not proc either of these since its coming from another source,
as for how you should build eve, the best things about hybrids is that you can build either way and you'll do fine, the major thing is though is you gotta change your play style depending on what your choosing.
if your going for an AP build then you'll want to attack agressivly with your abilities, you want to nuke and get out quickly. this is because majority of your damage is coming from your spells and once they're on cooldown, your damage is minimal unless you get a sheen item, but until then, using hit and run tatics works best.
if your going down an AD build, then your going to want to stick close because your probably gonna build a little tankier and majority of your damage is coming from your auto attacks. simple as that
in terms of sheen. I find that upgrading it last is the best choice. you can get much better items before it's upgrade that will help you a lot more than what it was going to give.
for the upgrade though the choice will depend on your AP amount. trinity force only gives you 150% of your BASE damage, while lich bane will give you 100% of your AP. so this means that once you hit max level, you cant increase your trinity force's damage while lichbane is only limited to how high you can bring your AP up. at level 18 you will need at least 165 AP in order for lichbane to provide you as much damage as trinity force. but lichbane also comes with 80 AP itself so in reality you need only 85 AP in order to match it before you finish lichbane
the reason why I say upgrade the sheen last is because for trinity force, the amount of the stats on them are going to be very small compared to other items you could have bought while trying to build trinity force, but those other items will give you more and you'll still have the proc of sheen.
hope this helps