Ordering of old domain is much better than new one. Old domain will give you better ranking as google prefer those domain which are old one, have better domain authority as compared to new one.
It vary.... yes domain age is important factor for SERP. But if some one / you have build the spammy links using the old domain, definitely it is not recomended. Yes there are various ways to deal with spammy links, but yes before buying domain take a look of backlinks. You can also check the archive by using web.archive.org.