Anyone know how to make opt-in email stay out of the spam folder?

So, I have a number of double opt-in mailing lists. This means these are surfers who have visited my sites, entered their email address, then received an email to their inbox, and confirmed that they want to subscribe. Yet it seems like more and more of my email is getting sent to the spam folder or utterly blocked by some ISPs. AOL regularly sends me these incomprehensible "email abuse reports" for my "FBL" and, although they redact the email address from the heads, all the emails I send include an unsubscribe link at the bottom, so I can see who AOL is claiming is complaining. When we've tried emailing any of those emails to ask why they complained, instead of just hitting unsubscribe, they have all claimed that they did not complain or in any way flag the email sent to them from my company.

So I am totally baffled and frustrated. I need to be able to have my emails arrive at their proper destination. These are small legit lists, numbered in the thousands of subscribers and not the millions.

Do I need special hosting or a specific domain to mail, even though this is 100% legal legit email and not very large lists? If so, what do I need to look for in a provider?

Do I need special software to have my proper emails get through to their proper recipients? If so, any recommendations? Keep in mind that these are not huge lists at all, and I don't mail all that frequently, so I don't need anything which is able to handle enormous traffic.

Anyone know any other suggestions for how to make opt-in email stay out of the spam folder?