A game-changing tool for thinking for me is mindmapping software. I recommend Freeplane https://en.wikipedia.org/wiki/Freeplane, released under a free license available on most operating systems.
It simplifies and clarifies without burden, enabling you to think about your work.
Does it support (or are there any others you've encountered that support) non-hierarchical links? A severe limitation of most mind-mapping software is that every node needs to be in its own little slot in the hierarchy; I don't think like this. I think in graphs, and interrelations – I suspect most people do. If I can't connect widely spaced nodes with some kind of edge, it's not a map of the mind at all.
Exactly my issue with all mind mapping apps I've tried - they are trees, not graphs, and I don't think that way.
I find them useful for to-do lists, but little else. Even if you can connect two separate nodes, the tool doesn't use that new information to change the organization of the nodes (something like a force-directed graph could be interesting).
Scapple just lets you draw nodes and edges. I fell in love with it a while ago and use it to collect my thoughts, and to put together project plans (treating it like a dependency tree, even though it doesn't impose that constraint on you)
I think Outliners are great for thinking and note taking.
For me tools to help me think usually means those that help in writing. Writing is thinking on paper, giving it a tangible form. You write after spending considerable time distilling your ideas and assumptions to a coherent form. However, the problem with writing is that it is time consuming. Anyone who has written more than a paragraph will attest that the important part of writing is to whittle away all the flab by editing to make your ideas clear to your audience. To make things clear often the writing needs to be reorganised because the vision of the writer can't always be conveyed successfully to the reader without considerable skill from the writer.
Outliners helps in this organising aspect. In a wordprocessor or text-editor you work with logical units of sentences and paragraphs that carries multiple ideas. It is not easy to mix and match stuff there as you need to rewrite them often which can become tiring. With Outliners, you can, in a way, do that. Incessant focus on features to reorganise ideas aid in creating logica arguments. Clarity comes with having an understandable structure. Outliners let you tinker with the structure without much cost. In a wordprocessor, cutting and pasting becomes tedious after a while. Outliners are built for moving things around. It is comparitively easy to move text around. Keyboard shortcuts are tailored to allow you to do it easily. It becomes second nature after a while and you feel constrained using any other tool.
Outliners use each line/bullet as the smallest constituent of the 'document'. It can be heirarchichal or it can be flat. Bullet points allow ideas to be concise. You can divide ideas to make small sub-chunks while your brainstorming sessions progresses. These programs allow them to be moved around and edited to make them fit with the idea you want to communicate. SInce each lilne only contains only one idea, it is easy to move them around without much editing. Good outliners (single pane outliners) allows features such as 'hoisting' (hides everything except the current idea under consideration) and sorting features to make thought creation and organisation a breeze.
Many 'outliner people' [0] will have a brainstorming session to get everything they have in their minds out in the open. Later they rearrange them in to heirarchies (paragraphs/headings) to make sense of them. You can sort, resort and arrange your ideas in whatever way you like.
Many people use this together with similar other tools like Mindmapping software, which accepts OPML file format as input, allowing work to be transferred seamelessly to tools that are best for the job.
It is sad that outliners are not seen wide adoption among people but they were big in the 90s and many were hit products (Thinktank, More, Maxthink). I can't even find good outliners now for Windows. Some exist for Mac (Omniouliner). Although I am a user of Org-mode in Emacs, it is not useful as a thinking and brainstorming tool as it doesn't have the ability (out of the box; anything is possible in Emacs) to move around stuff easily as in a dedicated outtliner.
I've recently tried a few different outliners and hierarchical thought organizing programs. It's an ongoing search to find the right balance of features and simplicity.
Nulis [0]
This is more of a hierarchical thought organizer than an outliner in the traditional sense. It is targeted towards developing and writing literature, and shows everything on screen at once in a series of columns.
I found it very easy to write things and break things down, but more as prose than as a series of items to be completed - good for brainstorming. It provides a checkable box via Markdown, but seems its not really intended as a todo list.
Quire [1]
I have had great luck with this app for the past few weeks in getting some big projects done. It's easy to enter things, move them around in the hierarchy with the keyboard, then treat them as tasks in a ticketing system with assignees, progress status, and notes and comments that support Markdown.
Both of these have JSON based import/export formats so it would be possible to sketch a design in Nulis, then move some parts to Quire for more detailed tracking of steps, via some kind of conversion script.
These are both web apps so available on my home and work PCs and phone etc.
old favorite Abstract Spoon ToDoList [2]
I used to use this a lot. It's a very capable open source outliner for Windows (and Linux apparently) with lots of different features and configurable modes. It runs as an app on the local machine but the data can be made available online via file synching services. It will only show the note for the current item. It has a very busy interface but can be stripped down to something fairly clean.
I am still on the lookout for a hierarchical design app that includes sub-trees of implementation steps per design item and related notes for all items. Sometimes I like seeing the text of all notes, and other times I want some or all hidden. The common paradigm in many outliner/todo apps is to show the text of the current note only, and I find this to be like looking at my design through a keyhole. I have started writing my own version of this sort of app a few times. It's hard.
Quire follows the show-note-for-current-item-only idea, but is still my current favorite due to its combination of decent keyboard short cuts, clean look, ability to share my status with my manager, and very active developers.
It simplifies and clarifies without burden, enabling you to think about your work.