Anything we send up to LEO now is 1,000$+ per pound just from getting there. Now picture something large enough for X people plus their decedents to live in for 10,000 years including redundancy's and manufacturing base and you get some idea how much this would cost as a baseline right now. Now, we need to add however much fuel it takes to get it moving and slow down at the other end. 100% world GDP for Y years is the kind of figure's you end up with.

However, if we start building stuff from raw materials found in space these costs should drop dramatically. Honestly, we are looking at hundreds of years either way so it's sort of meaningless with our current lifespan.

Well, really all three are due to insufficient launch capbility. We'll have to assemble the colony ship in orbit.

Really, we need to build the Orion nuclear pulse ship for heavy lift and intra-stellar transport.

Without a reworking of modern physics, the Alcubierre Drive for example, transport is going to take a loooong time.

Even if we didn't need a backup planet, this is the next phase is human exploration. It's inherently part of human nature to expand our prescense.

The won't be launched from earth or assembled in orbit from parts launched from earth - they'll be built from materials mined from asteroids

I wonder where the optimal location is to construct the first ship yard. Vesta, maybe?