If you move to the US as a non-US citizen, are you eligible to sign up to the new so-called 'Obamacare' (ACA) health system for medical coverage, presuming you're a resident? If not, besides becoming a citizen, is there any requirement one might need to fulfil in order to obtain it?
You're eligible to sign up, you're not eligible for the State/Federal assistance in paying the premiums. As long as you're a US tax resident (filing forms 1040/1040A/1040EZ, not the NR versions) - you're required by the ACA to have coverage either through the employer or through the exchanges or otherwise. But there are no limitation on your immigration status to buy a policy, in fact - many illegal immigrants can only have coverage as the result of ACA.