This assumes a software project of some sort while a lot of my todo's are non-coding (read prospectus X, have a call with lawyers re Y, analyze specific effect in Excel etc).
The stuff I trade has a fairly short shelf life, which forces me to spend a lot of time on R&D - not sure this is due to my creativity. I'll check out some mindmap tools, but from what I know about the concept it's not going to do exactly what I want
I have looked at Confluence. While it's probably a great software team management tool, it's an overkill for me. Plus, something like that would have to go through the firms purchasing etc.
The easiest solution is probably to maintain an Excel spreadsheet - I kinda-of already do that, just need to be more structured about how I represent things. I was hoping for a canned solution with a nice mobile interface but...
The same type of list can be done on your mobile using a "Sticky Notes" type app (text editing really). In fact, I maintain a list on mobile which I then manually export to PC. It'd be a pain to manage something like this manually on mobile, but maybe a task-app may be found, though I'm wary marrying tools like that.
For meetings and date-based events/tasks, use calendar, which you can access through both PC and mobile (ie. GCalendar or corporate Exchange/Office365). You'll get reminders and often you can find old items in the history if you need it later.
Mail is good for both communication
and personal notes, you can use tags/folders/colors to sort/prioritize them, and that too can be accessed from anywhere.
Main point is really, no tool will do the structuring for you, or "everything you ever need", without you losing control. Keeping the list short and non-complex is almost always better as individual capacity is best used for the most promising stuff. Do you want to do work by a task-list, or by using your brains and senses? Often we can provide more value by doing less, and doing the smart things instead. Sometimes, the smart thing is to get bored, or lazy, and then automate something.
Thunderbird and Outlook have tasks, and can be set to expire at date-times. It might even make sense to separate where you put what, as a too long list is just not that readable if you keep adding more items than you stuff away. Looking for perfection in the one and only tool is futile as there are so many different ways to do a "task list". Probably many apps for this that can be tested though, if you really need to marry something (which may later go away, or later turn out to have limited functionality anyway).
In the end, what brings value is actually having done the stuff, not managing lists. For R&D, learning by doing is very valuable, although not directly. When items are done, often that includes the documentation, so the item could even be permanently deleted as it's Done, or moved somewhere else.
Be wary: Whenever I start searching for "holy grail" tools that will somehow lift my burdens, it's often when I have no clue what I should be doing and would be better off talking to more people! When it's clear what to do, the tool become irrelevant, and just pick the best for the job, which is known enough to make meaningful decisions, and then progress or failure.