Or...you could be really daring & take the ferry across from Sirkeci to Harem...get to see Istanbul from the Bosphorous while sipping on a cup of tea & having a smoke!
If you do insist on taking one of the bridges then I suggest you go for the one you are closest to, as you'll prolly be sat in traffic trying to get to the other. Both bridges can get equally busy, but as said above the FSM bridge (aka 2nd) can snarl up pretty bad on entrance due to the bottle neck at the gise. If you do use the 2nd stay as far to the right as you can.
Also, feel free to use the hard shoulder while on the motorway, 99% of cops turn a blind eye.
PM me if you want any more info