Mac back up drive? What to choose...

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I have an older (512gig and likely at least 6 years old) Mac back up drive that is small enough it wants me to delete everything to deal with backing up the OS upgrade I just did. Nope not happening. Especially since my 6 year old macbook air is on its last legs (screen is dying and expensive to fix) so don’t want to risk it.

I have been reading reviews of “best mac backup drives” and there seems to be little agreement (I started to make a chart and gave it up because of that).

Probably be wise to get something 1TB to 2TB. I don’t care about speed as much as quality and reliability. Be nice if I could use it on both Mac’s and PC’s but not critical. I do have one PC back up one that I use when I am stuck using a PC (like when I have a work computer at work) and then to get files I need off of that to my mac play the flash drive transfer game.

Which brands are most reliable? Least reliable? Is there anything I need to know about buying one now since my laptop is old and likely I will have to buy another one in the not so distant future (unknown if a used or new one - depends on my finances and job situation).

My computer keeps telling me I have stuff on it that won’t be compatible with some 64 bit change. I have no idea if my entire computer (mid summer 2013) is that or the other 32 whatever it is. Probably be wise to get one that will work with future macs even if I have to get an adaptor now.

Any help/suggestions appreciated.