Is there a chart somewhere showing the time it takes to get the 1st confirmation as a function of transaction fee % or transaction amount?
1st confirmation is the next block your TX is in. It has nothing to do with the fee % and very little with amount transfered*. As long as the fee in comparisson to the size (in KB) is reasonable (according to miners) - which currently is 0.0001 per KByte - your TX will be in the next block (which on average are mined every 10 minutes).
What is the average BTC transaction time and what other factors influence it significantly?
Transaction time (as in the other party knows about it) is almost instantly. Confirmation time depends on the time it takes to find a block. This time is regulated via the difficulty to match 10 minutes on average.
* there is something called mature inputs which might allow you to send a TX without a fee. The idea is that big inputs (much btc spend) that did not get moved a long time need no TX fee.