Well, glad to see other people enjoying one of my favorite champs
Anyways, on to advice-:
You're going hardcore AP. This is generally lulzy, since your Poison can decimate squishies before they even realize it. HOWEVER, this becomes a serious drawback when you're playing against well co-ordinated teams. Why? They will rain CC from hell on you. Even with your passive, unless you get SOME tankiness, you WILL get killed. Singed is fast and durable, yes, but both don't count for much when you're getting super focused and don't have defenses.
Generally, I find a single RoA enough. However, if you feel you lack the oomph, go and get a Rylai's. That slow on it is unbelievable, and the HP is just gravy. With Fling, Mega adhesive, and a Rylai-Poison, you can pretty much guarantee kills on whoever gets caught.
Boots of Swiftness- Trade them in for Mercury Treads against teams with hard CC (we're talking 2+ stuns, or mega slows, or snares, etc.). Trust me you won't regret it.
Earlier I recommended Ninja Tabi too, but now I find that lackluster. If you're facing a DPS heavy team, Swiftness are better.
Warmogs is just fail. It makes you a meatball, and thats it. While Singed is one of the few Champs who can actually rack it up FAST, I don't think its worth the price. You'd do much better investing in the following items-:
Force of Nature: huge health regen, best magic resist in the game, moar movespeed. Whats not to like?
Banshee's Veil: when the other team starts raining all hell down on you for pissing them off, this is just sweet to piss them off even more.
Guardian Angel: just when they thought they had you...
Frozen Heart: hurray for Armor and mana AND cdr..
Archangel is... okay I guess. I mean it'll take forever to charge up, but even at base charge the AP bonus will be significantly huge (higher than Zhonya's afaik).
Starting items: Ruby crystal? Maybe sapphire would do the trick better, but its upto you I guess. I've tried a lot of different starts, and I generally find Singed to be pretty flexible on this.
Skilling order: Fling first is fine. After that, get Poison trail to level 3 ASAP. Why? Because a level 3 poison trail + fully charged RoA will kill all minions you poison. Just run to a lane, poison, run out. Bam, lane cleared. Next, get Adhesive to level 2. This is because the slow % at level 2 is large enough to usually guarantee a kill if the attack is co-ordinated (level 1 is a little chancy IMO). After that I suggest maxing trail then fling then adhesive.
Masteries- I'd recommend 0/9/21, to get Nimbleness in the defensive tree. This, coupled with a full set of evasion seals should net you 8%+ dodge. Not much, BUT if this procs, you get a 10% speed boost. Thats quite important IMO.
Summoner spells- CLEANSE! How can you ignore it? Its just amazing. People will be like "OMFG Singed STUN HIMMMM!!!" and you're like meh, whatever. Too useful IMO.
Ghost is just fine, pretty much mandatory on Singed.
This is just my opinion. I've been maining Singed for around 70+ games by now. I'm SL 20, but play often with level 30 clanmates. All of what I listed has worked for me. Hope this helps.