Sirchez just did a video about that, but I don't completely agree with him.
I suggest one of those Pages:
http://na.leagueoflegends.com/en/featured/preseason-update/8400-8437?build=30020041 Resolve + Precision: you can put anything in Resolve last slot, they are all good, and replace Conditioning with the appropriate other one in hard match-up in the second slot. In the first slot, Perseverance is all you need to keep running, but against teams with low CC, Font of Life is situationally super powerful. In Precision, Triumph is easy to proc on Singed and gives you big burst of Sustain in team-fights, and Legend: Tenacity, well, Singed loves Tenacity.
http://na.leagueoflegends.com/en/featured/preseason-update/8400-8437?build=30020162 Resolve + Domination: Resolve same as before, Domination for a more damage heavy build. You get Spellvamp and more AP to fuel your Spellvamp.
Resolve + Sorcery: Resolve still the same, and Sorcery, well, it's full of wonders... You can get any two among: more CDR for your R, Mana Sustain for lane, more MS + bonus damage based on your MS, a Magic Shield versus hard AP lanes, more flat CDR, early game poke, late game scaling, and MS+AP in the river. (Well not exactly any two, the ones on the same line are exclusive, but still...)
Sorcery is probably best for Splitpushing versus Precision for Team-fights versus Domination if you hope to snowball the game.
I personally don't like Inspiration so I'll skip it, but I'm sure you can also do plenty of fun stuff with it. Magical Footwear especially catches my eyes, except you often buy boots super early, so maybe not.
EDIT: oh and in the Keystone Slot in Precision, I really like Grasp, but Aftershock is good too. More team-fight oriented, though.
Now if you don't want to go Resolve Primary... I heavily suggest taking it Secondary for Perseverance and the 3rd Slot, but if you really don't want durability, you can still use the same Secondary mentioned above.
As for the Primary:
- Precision Keystones are all terri-bad (as expected from the ADC path).
- Domination: Predator is basically a Righteous Glory on your Boots, so should be great, but it's probably the only good Keystone here. Cheap Shot is great with Rilay, but not so much without, so go for Taste of Blood if you don't want Rilay. In the Hunter slot, you can go for Spellvamp or Items CDR, but Spellvamp is probably better in most circumstances. (Hum, does Item CDR work with Predator itself?!)
- Sorcery: well, as discussed in the Resolve Part above, Sorcery is full of stuff you want, the problem is the lack of good Keystone if you want to take it Primary. Phase Rush is not that hard to proc (E+aa+1 tick of Poison works), but you need to get in melee range first. Comet is horrendous (you basically dodge for your opponent if you E them), and Aerie is awful (you run away from your opponents most of the time so you don't pick it up early).
- Inspiration: don't like it, yadda yadda, try it for yourself.