I am working to get my bitcoin off of exchanges and into cold storage
Good decision because with this, you can be able to know the amount of fee rate you're going to be charged before making your transaction, but not only that, you could be able to customize that fee to your taste.
but I had a question regarding transaction prices.
There is nothing like transaction prices, what we have is transaction fee.
As more adopt Bitcoin, transaction prices are going to increase as there is more demand for blockspace. Is there any documentation or research into what transaction fees may look like in a world where Bitcoin is more widely accepted?
Its simple to know and understand, if the network gets busy, then there is more transactions ongoing and the mempool will be more congested causing increase in the transaction fee, in such a way that, anyone who can pay higher will get his transaction confirmed faster, which is normal on many settings as per competition, if there are no more clogging and pending transactions as before, then the network get less busy and no much congestion and we pay lesser fee, as regarding the block space, that is what we have for now, we cant predict the future if there could be addition or subtraction on that.