Doran's Ring - I usually start with this item because of all the great stats it provides. It helps with your domination in lane and provides you with health to increase your sustainability.

Catalyst The Protector - The passive from this item along with the health and mana helps greatly with your laning and team fights.

Sorcerer's Shoes - For speed and magic pen for greater domination.

Tear of Goddess - Mana is a really big problem with Swain so getting this item would help you throughout the whole game.

Zhonya's Hourglass - A must have item on Swain. When you use it during your ult, your ult doesn't deactivate, making you heal for a good amount of damage. This will help with team fights a lot.

Rabadon's Deathcap - More ap = more healing = happy Swain.

Archangel's Staff - More mana = happy Swain.

Void Staff - Get this if your opponents have a lot of magic resist.

Other Items to Consider:

Guardian Angel - A really good item to use on Swain. This will help you greatly in team fights and provides you with a good amount of armor. Replace with void staff if you are having trouble fighting against ad carries.

Banshee's Veil - Replace with void staff but get it whenever you need it if you are having trouble against ap carries.