I recommend always starting Gromp. After clearing Gromp/Golems kite blue/red buff but make sure it doesn't lose its patience bar. Do the same with the next buff and then back and get chilling smite.

Try to save your chilling smite for ganks. Your ganks depend on landing your snare. Pop poison trail and ghost if needed, then smite them, place down adhesive, and then fling the enemy onto your adhesive. EZ

Maxing out q 1st is pretty self explanatory considering it is your main source of damage. I choose to max out e instead of w 2nd because not only does e's damage scale but it also increases the snare duration. I like to take ghost instead of flash because catching up to people with fling can be difficult when your trying to gank a lane that isn't pushed up. It helps a lot with disengaging too.

Boots - Simple, take merc if enemy ap carry is fed/if the enemy team doesn't have many AA champions. Take tabi if the enemy team has a fed AD carry or has a sated jungler. You can take swiftness if the enemy team doesn't have enough AD/AP to melt through you or enough CC for the tenacity of mercs to be needed.

ROA/Seraph's/Rylai's - This is your AP core. ROA provides a lot of helpful stats for singed. Seraph basically lets you have poison trail on infinitely and gives you ap off the **** ton of mana you have. Rylai's gives you a lot of AP, some more tank and scaling for Cinder, and a helpful slow.

Tank Items - Frozen Heart is a great item on singed. It gives you A lot of armor and its passive is extremely useful for your whole team. It also gives you a **** ton of mana which scales off your passive and seraphs if you chose to take that. I would always take it unless the enemy team has an extremely low amount of AD, which is not very common. Righteous Glory gives you a good amount of mana, lots of health, and, most importantly, an active that extremely helps with engaging. I would take Randuins if the enemy team has a 2 champions that crit (like yasuo or trynd on top of their AD carry) or if a vayne is wrecking havoc. I would take Dead Man's any other time because the movement speed really helps. Banshee's is your go to magic resist item. Not much to explain.