An LMO is needed to apply for a temporary work permit. To get an LMO, the employer has to advertise the job to prove there are no Canadians available for it. I've heard it takes 6 weeks after the advertising of 2-3 weeks is already done.
An AEO is needed to apply for immigration as a skilled worker from outside Canada or you could also use it to apply for immigration under a provincial nominee program. To get an AEO, no advertising is required. It is generally easier to get an AEO than to get an LMO. Many employers who have been denied LMO for a worker have been granted the AEO.
Either an LMO or AEO will work for you. If you get the LMO, you would apply for a work permit, go to Canada and work and apply for your PR later.
If you get the AEO, you apply for your PR directly and once you get it, you can come to Canada and work anywhere, not just your relatives.