Is there a rule of thumb for what fee to set when the network isn't congested vs when it is?
What do you define as a not congested network aka mempool? It's highly unlikely that there aren't enough transactions to fill a few blocks with a minimum relay feerate of 0.1sat/vB, especially with all this Runestone crap and whatnotelse.
So, I predict that mempools won't dry out of transactions for a long time. There will likely be at least enough transactions in mempool somewhere in the ballpark of 25-45 blocks worth of space for quite some time (weeks, months). Most of them will be in the very cheapo camp of 0.10-0.21sat/vB and will take a long time to be confirmed.
If you want orientation have a look at the transaction fees prediction of mempool.space which is usually quite good, see screenshots of current state below.

For context, these are the candidate block and a few of the last mined blocks.

Highlighted are the minimum feerates that made it into blocks. I would have a look at those and maybe take the average of past few minimums, omitting extreme values, and add maybe 10-20% if your goal is a confirmation target of next one or two, maybe three at worst blocks.
If your transaction isn't urgend, go for the low priority value of mempool.space. The "no priority" value might take very long to be confirmed, days or even weeks. Currently a feerate of 0.2sat/vB isn't likely to be confirmed in weeks and many nodes have a default setting of dropping a transaction after 14 days of not being confirmed in a block unless it is rebroadcasted.