Well, you can store and accumulate your fish at home or in your bank, but they actually have to be put into the crates in the boat, for the quests to be turned in.
As a result, you'll want to place the Tokuno boat with your fisher (it gives a +1 to fishing when fishing off its decks) in trammel or fel, and keep it refreshed. I think you can place the Gargoyle boat with one of your other characters and still use it, but each character is limited to one boat (not counting rowboats), and only one tied specifically to the fisher counts (for its location) when getting a quest.
To clarify point #5 in Lestat's quote of my old material, if you accept the quest (so that you can see what it will actually require), then reject it from your hold, it counts against you. If you simply do not accept a quest from the start (rejecting it sight-unseen), it's not supposed to have an effect. They were bugged on the release of High Seas to where they would hurt your standing on any rejection, but that got fixed (along with a related issue where the lobsters and crabs were bugged to given only the point value of shallow water fish - though they are still really undervalued in the opinion of most fishers, due to the effort involved).
To clarify point #3 im sos440's post, there are a LOT more options for dungeon fishing if you have Time of Legends. It turns out that NEARLY ALL OF EODON counts as "Dungeon" for fishing - and you can also use the lobster traps from shore in all dungeons (and Eodon) as well. Unless a dungeon fish is specifically found in only one dungeon, you can take care of most of the dungeon fishing (and crabs/lobsters) with a pack animal in Eodon, as there are several long stretches of river where the only spawn on one side of the river are corpsers and vampire bats (with the occasional saber-toothed tiger, which appear to be non-aggro, or at least low-aggro). Plus, you can rez at the kotl city turn-in NPC (while he lasts) or any number of wandering healers.
For that matter, the shallow water fish are located near shore in every facet except Eodon, near some server lines, and occasionally other locations (there's a shoal off the east coast of Serpent's Hold that counts as shallow water, that goes out several times the normal distance for shallow fishing. So, you don't actually have to fish from shore for them, but can park close to the shore (or in a special area) for it. My personal favorite for shallow water fishing is the river south of the Ter Mur royal city, but that's because it's a relatively safe area, and I can walk back to my 2nd house there, and take a teleporter trip back to my fish stockpile to drop off, without having to cast spells), and the Ter-Mur specific fish can be caught in shallow water.
Note that once you get the ability to fish dungeon fish, it will seem your quests will get a setback.
This is because of how quests work.
Essentially, quests all start as 1-liners, where only one fish type is asked for.
The quest system then keeps track of how many fish/crustacean types you've completed quests for, and also if you've failed quests by losing (when a ship goes away from not being refreshed) or tossing the crate.
The chance for a second line, is the percentage of fish types you've filled a 1-liner for, times some number that approaches (but isn't) 1. So, even if you've filled 1-liners for all possible fish types, the chance of a 1-liner becomes small, but still exists.
The chance for a 3rd line works the same way, based on the 2-liners you've filled, based on the fish type.
The chance for a 4th, 5th or 6th line work the same way, based on how many you've completed for each fish type of the previous level.
There are 12 shallow water fish types that fit quests
There are 12 crustacean types that fit quests (6 lobster, 6 crab)
There are 18 deep water fish types that fit quests.
So, before you reach the ability in the low 100s to fish in dungeons, the calculations above are based on X/42.
But, when you gain the ability to fish in dungeon waters, the 12 dungeon fish enter the equation, and the variables switch to X/54, and you start getting a lot of 1 & 2 line quests again, until you gain experience filling quests for the new fish.
Eventually, you'll get to where 1 line quests pretty much disappear, and 2 line quests become rare again (but not impossible). I've had 120 fishing now for 7 or so years (though I stone it off for spellweaving some of the time), and still get 2-liners on rare occasions when I put fishing back on the character (like I did for all of April through mid-July). Most of the 20 or so quests I did (trying to get a PS for a new friend; didn't get a 110 or better, as we'd already gotten them a 105)were 4-6 liners, but I did get a 2-liner and a 3-liner in the bunch.
If you do stone fishing off, remember to always add it back to the same character, as the PS stay with the character, and if you click a fisher NPC for a quest with fishing off, it might accidentally reset all the fish counters in your quest system to 0.
If you get a bunch of PS 105s, but not any better, just stockpile them until you get enough for a scrollbinder to make a 110. If you get the 110 before you get enough 105s to bind, either give them to other fishers or turn them in for cleanup points. Do the same for each level of PS, though you're much more likely to get a 120 PS drop before you ever get enough 115s to combine for one (but I saw it done at least once, but the result of several fishers pooling their extra 115s to get a 120 for a colleague).
I'm so happy. Now I have 10 more points to go to hit my cap. 
I'm so happy. Now I have 10 more points to go to hit my cap. 
I am at the bus stop right now but I'll put this into practice tonight when my chores are done.