Don't have to go with Bloodthirster but I find the increased lifesteal usually helpful. Can also have Sanguine Blade if on other maps. Can also get Phantom Dancer for the increased critical chance or sell your Berserker's Greaves to get an item like Zephyr. It depends on the enemy though like if they have lots of CC.

Usually go with masteries such as those that give Ability Power, Attack Speed, Armor Penetration, and Magic Penetration. I go with these masteries because my Teemo is sort of a hybrid with the magic damage done by his Toxic Shot, Wit's End, and Malady.

My Summoner Spells are mostly those that will help me survive with Flash and Exhaust. Barrier is also useful and Ignite helps to ensure the kill. Heal is also useful but there is also the effect of decreasing all other heals from allies.

For Farming you want to slowly poke the enemy and deal damage to them with your poison. Keep up your constant movement and pop out to last hit a minion. On maps such as Proving Grounds and Dominion this isn't as important due to the more gold you get but it still a good habit to learn. In teamfights you want to stay at a safe range and use your abilities wisely. Use your blind(Q) on their ad carry and don't be afraid to put a mushroom down during a teamfight.

Use your Mushrooms in place of wards and always place a few near your turret itself just for those occasional tower dives.