I bought a new domain from an auction that I migrated my site to and I am getting a lot of 404s from links to whoever was previously on this domain.
In this case, the 404 response is arguably the correct response. Correct for users and search engines. (You could even send a stronger / more deliberate "410 Gone" response - after all, these pages are not coming back it seems.)
A redirect only really makes sense if the content has moved to a different URL, or you have similar/related content at the new URL.
Redirecting users to a completely different page that is unrelated to the content they are expecting is confusing. And consequently, most users are likely to just "bounce". A better response would be a customised 404 that explains why the page no longer exists and tries to get the users attention in other ways, perhaps suggesting (some of your best) pages on your site that they may find interesting.
Redirecting search engine bots to a completely different/unrelated page is likely to be seen as a soft-404. But also, redirecting many URLs to a single page is very likely going to be seen as a soft-404.
So, you are not going to gain anything by redirecting in this instance and it could even be a step backwards.