To play Blitzcrank you have to be very patient, because with a single grab you can cause an ace on any team, so be patient and wait for the right time.
Blitzcrank its very hard to play if you want to kill all enemies alone so dont engage unless you are sure you can kill and get out alive.
And never forget that you are a support so dont KS your carry or the game may be lost.
Also dont forget your passive can help a lot in fights, the enemy think your gonna die and you get 50% of your Mana into HP for 12 sec, its time to run or to finish the job.

For Runes i use Greater Glyph of Potency but i didn't found them so i used Greater Glyph of Force. Greater Glyph of Potency will give you 1.19 x 9 AP and with 3 Greater Quintessence of Potency x 4.95 you will have 26 Ap + 15 AP with a Doran's Ring and Masterys you should start with about 47 AP, when you will need it more to do some extra damage on your Grabs, so you can get some assists or even a kill.

You must know that this items are very expensive and you're right, its more than 16k to finish the entire build which for Blitz is a lot of gold and you must buy the right items at the right time.

First buy Doran's Ring and if you can get back to buy boots of speed and 1 or 2 wards but dont waste more gold on pot's or other staff because you will not need anything else now.
When you reach LvL 6 farm as much as you can to get 1600 gold and buy Needlessly Large Rod to give you an huge boost of AP and let the party begin. With your grab, fist and ulti you will do a lot of damage and your ad carry should finish the job very fast.
Next get Ionian Boots, Tear of the Goddess, spamm your Overdrive (W) to start stacking mana and get Nashor's tooth and sell Doran's Ring.
Then buy Frozen Heart and Archangel Staff. If you can finish Rabadon's Deathcap and Buy Lich Bane.
Now you will see the real use for Lich Bane and his passive that dead 100% damage of you AP after you use an ability, and you should have about 650 AP, cooldown Reduction is 70% and 1,5 AS with about 120 AD. Now guess what happens when you use combos like "grab + autoattack + fist + autoattack + Overdrive + autoattack + ulti"

When starting teamfights dont even think about grabbing the enemy tank or your team will focus him and you all die, im sure of that because i know from experience so it will be a good idea to grab them carry and fist to get a fast kill.
In gank's always try to use this combo "Overdrive + fist + ulti" and then do as much damage as you can and if the enemy try to escape use your grab or you can use it to do an huge damage and kill him .When defendig a turret at the start of the game and you are alone wait for them to "dive" the turret and then use your ulti to kill really fast all the minions in the zone and grab an enemy and fist him and your turret will be your best friend, this is teamwork, Blitz + turret = OP