When things start happening regarding Asgardia's ability to put it's first habitats and Asgardian citizens in space, the first thing that needs to become operational is a sophisticated laboratory that monitors virus and bacteria mutations that could affect life of the space inhabitants and life on Earth as well. Apart from monitoring this lab would also work on prevention and containment of outbreaks, i.e. invent vaccines and establish quarantine protocols.
As for surgeries, at first we will not have enough people and infrastructure up there to be able to have all the specialists required to respond to every possible emergency. That's were technologies such as remote surgery (already exists) will help. Surgeons residing and working on Earth will be able to perform surgeries on patients in LEO.
One other thing that would be very helpful to people living in space would be larger tolerance of radiation. I don't know when or if this will be possible, but if we can do this through genetics it would be great.
Finally, while we do know of the negative effects of zero gravity on the human organism, we do not know what kind of effects low gravity would have on our bodies, although if we take the zero gravity effects as an indicator, they're probably not going to be good. That's why I think we should not make Moon, Mars or colonies on other bodies.
Instead we should focus on spinning space stations like the one in the movie Elysium in the orbits of these celestial bodies. We would still have industry on them (planets/moons) but we would not live there. Most of the work on these industrial sites (mines, refineries etc.) would be done by automated machines (drones, robots etc.). Human intervention would be mostly done by remotely controlling these machines, or even robotic humanoid avatars, when needed. Very rarely would we have to physically go to the surface to do some work.
And this is not just my conclusion and opinion. Apparently scientists looked into this decades ago and came to the same conclusion, that space platforms are the best way to colonize the solar system, while exploiting resources from the celestial bodies. For more on this look up a TEDx talk titled "How and Where to Colonize Space" by Joe Strout.