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For 80k I would recommend using an email service provider (ESP). It will manage all the email things you need (unsubs, bounces, actually sending the email) when sending to more that 1k email addresses.
The good low cost ESPs are:
www.constantcontact.com – Offers a free trial for a month I think.
www.mailjet.com/pricing – Really easy to use (I use it now and then). Monthly price
www.aweber.com – $1 trial, but not sure of list/subscriber size. I also use this one.
All of the above will make you use a unsubscribe link. It is the US law (2003 CAN-SPAM act). They will give you one that you can put in the email footer and then they manage the rest.
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I ended up going with mailjet.com
I did have a problem because I moved the mailing list over from infusionsoft and I have a HUGE bounce rate which directly limits the amount of mail I can send each day. BUT I highly recommend them.