Regardless of where the income is coming from, it's a minimum 4-5 year wait to satisfy the 3 years income requirement, wait for final tax returns, and enter the lottery. If not chosen in the lottery the wait can be much longer, maybe never being selected to apply.
Regular visitor visa is your only option. If it's accepted, they can come visit you in Canada and try to extend their visitor status as it comes due. Once you get a job meeting LICO, you can apply for supervisa for them for extended stays. As mentioned they'll require emergency medical insurance, and costs for this will vary depending on their age and health. It will probably be at least a couple thousand per year for each of them.
If their TRV is denied, they must stay in home country while you move to Canada. If this is not acceptable to you, then you will really need to re-asses your priorities here - establishing life as PR in Canada or caring for your parents in home country.