Cyber Monday should bring some deals. Other than that, shopping right after the new version is released is the prime time to score a great deal on the older model. I've also bought an Apple refurb and been very pleased. It comes with the same warranty as a brand new phone if purchased from Apple or one of their authorized dealers.
Like MiketheGrinder said, Cyber Monday (and Black Friday) almost always have some great deals. I got my Google Pixel last year for a really amazing price. I also agree that getting a good deal on a phone is affected by the newest version coming out. However, I think the cheapest prices, at least for Apple, tend to fall between the time between the announcement of the newest version and its release date.
It's Cyber Monday today! Lots of good sales going on right now and you can shop from home! I see that there are some BOGO deals with cellphones going on right now. If I were you, I'd look today for a good deal.