Most aged-domain deals start in a spreadsheet. Someone sorts by domain rating or referring domains, picks a handful of names, and plans a 301 or a rebuild. That order is backwards. The links only help if they still belong to a site whose topic, language and history match the job you have in mind.
I have bought names that looked strong on paper and then opened the Wayback Machine. One had been a careful local blog, then a parked page, then a list of casino keywords. The referring domains were still there. They were just pointing at a past I did not want to inherit.
What the archive usually tells you first
You do not need a complete capture history. Three or four snapshots will often do: an early useful one, one from the middle, the latest one, and any point where the pattern breaks. Look for a language switch, a sudden change of topic, long stretches of identical parking pages, or a redirect to a host that has nothing to do with the old site.
A quiet, consistent archive is usually a better sign than a huge spike in captures. Spikes often mean generated URLs, not a busier publication calendar. Empty metric panels are not a clean bill of health either. Some messy histories leave almost no footprint in Moz or Ahrefs, and a buyer who stops at those numbers will miss it.
When a 301 is the wrong next step
A redirect onto an aged domain can pass useful signals. It can also pass a topical mismatch, a spam neighbourhood, or a language the new site will never use. If the old site and the new one do not share a topic, I would rather register a fresh name than spend the next few months explaining the history to a search engine.
The same caution applies to a rebuild on the same domain. You are asking visitors and crawlers to treat the new pages as a continuation. That only works if the continuation is honest.
I do the first pass in a place that already lines the archive up with the usual SEO metrics, then I still open the snapshots myself. Expired and auction domain research is how I keep that first cut short enough to finish before the auction ends. The decision still belongs to the archive, not to a single score.
If the snapshots, the live page and the metrics disagree, find out why before you bid. A name is cheap only if you do not have to unwind it later.