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.
1. Incredibly expensive.
2. Massive beyond the scale of anything ever assembled in orbit.
3. Big enough to carry a self-sustaining colony, above minimum population size for genetic issues.
So, newborns in zero-g, not necessarily needed, if we're really going to the stars the old fashioned way.