I have heard that using printer paper (non archival) will damage coins over time. Is this true for AE coins? If so, how long can I safely store my coins with printer slips before switching to archival based, acid free paper?
Personally, I think the pearl clutching panic over non archival paper is overblown. I don't recommend using it, but it's not going to destroy your coins, perhaps only tone them up a bit. Keep in mind many collectors in the past stored their coins in non archival envelopes and the coins have reached us none the worse for wear.
Non-archival paper will destroy itself long before it will do any damage to your bronze coins. It will cause silver coins to tone, though.
I use the paper envelopes. I got tired of the plastic flips cracking after a short time, plus there is more room to write down the attribution. I like to hold my coins in hand from time to time, so I don't like slabs either. The few I have purchased have been "freed".
I store my coins in lighthouse trays with a paper slip underneath. Just in the off chance that the paper could damage them, I cut up flips and place a piece of the plastic between the coin and paper.
White paper in the past was worst than manila stock, it was processed with acid process. Today, it is all base processed. White paper today is actually mostly clay by weight. Burn a printed page of it some time. Only some burns, and you can still read it. Therefore, there is almost nothing left in copy paper today that will damage coins. I would have absolutely no fear of using modern white paper around coins, but manila envelopes will tone them. One of my prior companies was a paper distributor and I went to "paper university".