For me the best order is:
settler (to build roads and transform forest/jungle/swamp), Colossus, 3 trade routes, library, Cope's, university, Ike's. You want to build Ike's after the library and university, because Ike's only affects library and university output, not total science output.
The other thing you need to figure out are when to build the financial improvements. I usually build a marketplace just after Cope's (I find I really need to race to get this wonder; sometimes I even have to delay the library until after it is built). I tend to build a bank and a stock exchange as soon as they become available, since, unlike Cope's, Ike's is a low-priority AI wonder and you can afford to delay it while using those caravans to build higher-priority wonders (Leo's, Mike's, Adam's for me). Superhighways and SETI get built as soon as they become available.
Last thing I'd recommend is, if you're on water, make sure you have a harbor built before you start celebrating WLTxD in Republic/Democracy. It's a mistake I made alot at first; I'd start boosting city pop and run out of food almost immediately
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Dig trenches, with our men being killed off like flies? There isn't time to dig trenches. We'll have to buy them ready made. Here, run out and get some trenches.
-- Rufus T. Firefly, the original rush-builder