I'm personally looking at traffic overtime, I want consistent traffic increases over a period of years to essentially demonstrate that google likes the website. Any crashes in traffic is a red flag, stay away. This is most likely a penalised domain.
Next up is outbound links. Link juice is real, and sites with tons of OBL's don't offer too much power. This is why solid PBN's give you a backlink on their home page and limit the amount of outbound links.
Next up, wayback machine. Anything dodgy happening overtime with the domain?
Anchor text ratios. If people can't manage their anchor text ratios properly in accordance with the penguin algorithm, I want no part of that site.
Referring domains - Obvious one, powerful RD's with no spammy sites. Especially any Japanese or Chinese backlinks.
Backlinks overtime - I avoid sites that have significant increases in backlinks at one point in time, this is clearly unnatural.
Note: Please make sure you are using tiers for safety if you care a lot about your site.
