i usually use meki into chalise of harmony, bloodraser, blood thrister and somethimes infinity edge and boots. it works most of the time.

Depending on whether your team needs you as support or damage, go

Chalice->Starks->Aegis->Survivability/Whatever

Chalice->Bloodthirster->Survivability/Whatever

You don't have to have a Chalice depending on your playstyle. You may just stack Bloodthirsters if you want to.

I picked up Sivir on saturday and this is what I run:
Meki with 2 pots
Teleport back to get Chalice & boots (normally beserkers, but depends)
Starks
Aegis
Last Whisper (armor pen works on towers apparently)

Runes I use attack speed marks, dodge seals, mana regen / lvl glyphs, Flat HP quints

Masteries I use 8-22-0 build. Offencive I get crit and Attack speed. Defencive I get armor & MR, dodge, nimble, hard skin, Veterans, Ardor and Tenacity.

I feel I do really well with this build, I hope this helps! Also pick up golem buff around level 7. Good luck