It depends. If you're a pro and lane swapping, you go Pickaxe or BF sword into shiv and then finish IE. The pick/BF is decided on how much gold you have on your first back. The reason why people get the pick/BF is because it gives them the extra AD so they can actually last hit minions without having to worry too much and then they buy Shiv. If you really want to go shiv first, you SHOULD get a BF or Pick. The shiv will be better if you can complete it early and are actually trying to "force" an objective, basically the only one that should be available at that time being dragon. If you have the shiv for dragon, then you as trist will probably be able to make somewhat of an impact. If you can end up taking dragon without it, though, IE would have been better. Whichever you rush, just make sure you go the other second.
Also, it doesn't matter what your friends say as its interchangable. I've seen people build it both ways, so just do it to your preference. If you actually start feeling that its not working too well for you, trying switching it around to see if you get better results.