The second option requires a bit more time and effort than a 301 redirect. You could do a mini overhaul of the site and turn it into a microsite for your main domain. This option is good for exact-match domains for your targeted keyword, and there are other reasons for going the microsite route that Rand's highlighted in his post about root domains, subdomains, subfolders and microsites. This strategy also works better if the old domain has decent rankings for the keywords you're targeting.
We do not only have Expired Domains, but you can also find lists of Deleted Domains for a lot of TLDs. Deleted Domains or Dropped Domains are available for registration and can be picked up for just the normal regfee at your preferred domain registrar! All Domains have the typical SEO relevant data, like Number of Backlinks, Archive.org Birth Date and a lot more.