I think FLyWright beat me to it. but still
http://www.trawlerforum.com/forums/s59/essential-tools-19932.html
As for power tools I leave them at home with a few exceptions as my boat is small enough that storage is really at a premium. I do drag my 18V drill and my good meters aboard when travelling fro more than the weekend.
You comment about the multitool and a sawzawl [ or a mini battery type Skil saw] may be valid but you might also CONSIDER leaving those alone UNTILL you find the situation where they are actually needed. Do your research and questioning to determine which you prefer or you may find what you think will be needed and what are actually needed are two different things.
There are so many small, battery operated handtools available now the choice is almost boggling and you can do amazing work with them and some attention. The only thing you will need is a means of recharging them effectivley.
When you do buy tools buy decent quality, not cheapie, as those tools often can cause more trouble than you realize when they monkey the very part you need to undo/remove. You don't need Snap On either unless you simply want those. I like S.O. Lots of good tools out there without the pricey stuff.
I changed to plastic tool boxes years ago as the only place I can store things is in the engine compartment and there was enough moisture to rust the metal boxes. I ruined two nice boxes so won't do that again. I periodially spray the boxes, while open, with WD-40 or the like.
If you are lucky enough to have GOOD space for a real chest great but then pay attention to mounting and keeping those drawers/doors securely shut.
For electrical crimpers, didn't cover it before, I use many but the Ideal Crimpmaster series are good units that will not cost a bomb [expensive enough] but do an excellent job. Do not go cheapie here as your electrical work really depends upon good work.
I'll say it again. Do not be in a rush to buy all now.
And ask about specific item when you have questions.