Check the 600 backlinks of the expired domain and see if you think they would be beneficial to your website. If they look relevant, clean and good, 301 redirect to your website.
If they maybe look a little spammy or wouldn't fit good into your money website backlink profile, create some content and backlink it to your money website and turn the 600 backlinks into tier 2.
Why do you think so?301 is fine but it looses juice after few days
What about the hosting...if I host it on my same plan as money site it will have the same IP right? Should I get a new host for that domain or is that not very relevant?if old link relevant to the new then 301 redirect is the best way. all the backlinks will be there and you will not be lost your ranking in search engine as well. Sometimes it just take no time to regain all the link juice but sometimes it may be bit late.