Personally, I do web-dev as my day job and game-dev as a hoby. For that reason, I use JetBrains IDEA at the company (UI + Java or NodeJS server), JetBrains WebStorm at home (UI + NodeJS server) and JetBrains CLion (Rust, C and C++). In addition to that, I usually use Kate for quick text editing. JetBrain products are paid products, and I pay for them because I earn money with them and need professional tools. As for CLion, I paid, because it's not expensive at all and I am willing to put a bit of money into my hobbies. Before I started using paid products, though, I used NetBeans, which is highly underrated imho. It is still actively developed, though not by Oracle anymore (which might be a good thing, actually; old website here).
The reasons to choose these tools are mainly because they are very feature-rich, providing everything I need, in a very easy to access, intuitive and clean fashion. Also, they all are cross-platform, which allows me to have the same development environment across Linux and Windows (without using Wine).
Now, let's take a look at your requirements and see how my environment would fit the criteria :)
I've considered a true IDE like PHP/Web Storm but haven't taken the leap
While using editors with plugins will get you through most small projects, having a full blown IDE will greatly simplify everything. An IDE usually is set up for a quick start with a pleasurable usage (lean interface with all the right knobs in all the right places) and has very simple menus to config some aspects. You usually also don't have to worry about setting up stuff like installing dependencies, setting up debugging or how to make the project configuration portable for all your possible editors or setups. You install the IDE, and it will just work(tm). There are people who like to puzzle together their IDE, and while I like doing that for my OS (Gentoo is one of the most masochistic experiences so far, but still my main system), I really enjoy having a comfy time with my dev-tools. I recommend going for an IDE (maybe a free one) and see if it's the right thing for you. What do you like? What do you dislike? What are you missing in comparison with an editor, like Atom? You will have to find out for yourself, if you really want an IDE or do the tool integration yourself.
Working with the web either managing a website or web application
For administrative tasks, you don't really need an IDE. Any text editor should be enough to edit config files. If you use a Windows server, Kate is a nice tool, but you might be more accustomed to Notepad++. MS Notepad, in the latest version, finally received support for UNIX line-endings, so that should work, too (finally).
Editing more than just html and css
What exactly is "more"? JS? Python? Kotlin? Elexir? Go? For HTML and CSS, a simple text editor with highlighting is enough, so Kate would fit the bill. If "more" means you also want to do a lot of JS or TS, then WebStorm is a very nice IDE which supports all the latest features and has awesome autocomplete (given you document your code using JSDoc or TS definition files). I never really tried anything else with it, but there is a whole load of plugins and you can go wild!
Regularly debugging a programming language like JavaScript, PHP, or Ruby on Rails
I just re-visited the whole JetBrains licensing model in order to answer your question. It is complicated. You either buy PHPStorm and RubyMine, or you get IDEA, which has plugins for everything JetBrains has to offer (with the exception of Rust debugging). IDEA is expensive, though, and you might get discounts for licensing more than one IDE. Personally, answering this question made me realize, that I should prolly re-visit my subscriptions and check if I am still using the best/cheapest options...
If you want to go the free-way, NetBeans provides everything you need. I do not recommend Eclipse, as it is cluttered and very non-intuitive. It is slow and stutter-y. Many people say good things about Visual Code and Atom, however I never got along with them and in the case of Code, Microsoft has a lot of suspicious license clauses imposed on you, so no thanks.