I'm also still learning, but might have a couple of suggestions.
Guessing that you aren't tooling since the leather is predyed.
Even with predyed leather, it might be smart to put a small test amount in a pocket of a pair of pants you don't care about and leave it while doing daily life. Sometimes that dye can bleed and you don't want ruin family/friends/customer's clothes or purses.
For a matte sheen, that is semi water resistant, try tan kote on a test piece and see how you like it. If you would like something much more water resistant and with a higher gloss/ sheen, try Resolene.
I have not used it, so I cannot personally vouch for it, but I know a lot of makers swear by Sheridan RTC.
As far as oils, I prefer olive oil and neatsfoot, but I tool almost everything that leaves my shop. Mink oil almost feels too greasy for me so I only use it for water resisting my husband's boots. Maybe I need to switch up my brand though.
Your burnishing idea seems like it would get very glossy, especially if you sand your edges as well.
Whatever you choose, I highly recommend testing it out and putting the test piece into use for a day or so. Best of luck!