Fragments/secrets
With the minimum pages(25), exploring all current locations nets you 17 or so secrets. Pages 100 would get you roughly 19 secrets
Options upon dying
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Save your charts – Just what it sounds like, it keeps your maps. Semi useless unless you’re still not clear on where everything is, will become more interesting when randomized maps are a thing. THIS OPTION ENSURES YOU WILL GET NO PAGES FROM ALREADY EXPLORED LOCATIONS, WHICH MEANS FAR LESS SECRETS GAINED PER CHARACTER.
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Save a crew member – Does what it says on the tin. Possibly useful for certain crew that are difficult to obtain? I’ve heard of people saving their magician friend guy dude man thing.
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Save a stat – Pretty much the only option I choose. In fact I recommend just dying with your first character, and choosing this. Then when you start up your heir you have two level 50 stats, rather than just one. This may be a bit gimmicky, but raising stats is particularly time consuming when compared with the 2 hours max to explore the entire world, or the "visit home port till you get the officer you want" which could take a while but normally not longer than 25 points of stats.
House/Heirloom
Pretty much just your house, and heirlooms save between deaths, if you have a will.
YOUR WILL DOES NOT SAVE. You will NEED to pay another 200 for another will upon death. If you do not have any heirlooms upon death, do whatever is safest to get 200 gold and pay for it again.
The option to sell heirlooms still exists for your character even if you don’t die.
Heirlooms sell for an average of 1k. You can store 11. On my test of selling all 11 off I ended up with 10424 gold. Small sample size but should be enough for general information.
Bought ships definitely do not save upon death.
Optimization of death
Clearly if you’re going to die, the best option is to have spent all 17 or so secrets improving a stat that you started at 50, passing down a level 67 stat to the next character. That character could again, gain those 17 secrets and after 4-5 characters you could have a 100 point stat passing down every time. This of course is assuming you get an officer able to improve the stat you care about.