Yeah that is a pretty common, suggested way of becoming immortal once we are able to store our consciousness as digital data. The idea is that stay in a body (biological/mechanical) as long as that body can sustain you and after it no longer can, simply move on to other body. As simple as that!
I will certainly watch Altered Carbon now as I am really interested in this subject and I hope you complete the Black Mirror series as well because even though it can be very negative, it certainly presents ideas that are VERY possible in the future, so better stay informed and think about it.