The depends upon the applications you want to use for each function, not only which OS they support but also, if there is a reasonable expectation that you might want to update those apps in the future, or switch to different apps for same functionality, then for how long into the future any particular windows version will be supported. The decision is much simpler if you are set in your ways and not the type of person always wanting more from an app, so feel the need to update, or just want to do it for the sake of doing it.
The browser in particular is what I'd focus on because it exposes you to security vulnerabilities in a dynamic way because any website can theoretically become compromised even if not set up to be malicious intentionally, so you're going to want a not-too-outdated browser, perpetually updated.
MS Office, similar situation but I find there are two cases for my modest needs.
1) I like a lightweight, non-cluttered, fast loading version that makes the most compatible files. Some people just save to non-MS-proprietary file formats for their own use or outgoing files, so I often find myself using Office 97, but for incoming files, somewhere around the '00s decade, MS added support for, and set the default file save format with an x on the end, like word *.docx or Excel *.xlsx, so if I could only have one version of MS office, it would be one new enough to support those, and with a toolbar you can live with. I hate the modern (ribbon?) MS Office toolbar but some people don't.
Small Internet Store, I have no idea exactly what you mean. I'd think that if it's not a browser based management interface, that you might just need basic web tools like an FTP client? Certainly any popular OS will support the latter.
It would be easiest to just tell you to get the most modern OS that has computer hardware support, and runs at a reasonable performance level, with a secondary concern about what GUI you prefer and how much it can be modded to be close enough to perfect - since none are perfect. However you are asking in the Win7 subforum on "sevenforums".com, so presumably you have an interest in it being Win7. Within that context, frankly I don't recall all the features stripped out of Win7 Starter or Home Basic so would avoid those, nor would I feel it appropriate to use Win7 embedded, and one of those mutilated distros like Win7 Lite where a 3rd party removes things, often leaves out things that later on, you'd wish you had. I'd also go for an x64 version because Win7 runs much, much better on more than 3.
GB of main system memory.
Any of the more featured Home Premium, Pro, Enterprise, Ultimate, should be fine for the tasks listed AFAIK, though as already mentioned, there is an expectation that Win7 and 8 will lose app support far sooner than Win10 so it really depends on how forward thinking you are - and also remembering that you can always switch later, and may need to anyway because hardware has both a finite functional lifespan and a finite reasonable-use lifespan when newer hardware becomes affordable and at multiple times higher performance levels but does not have drivers available for older OS, though the tasks you mentioned don't particularly need much performance, unless you like browsing sites with a lot of animated advertisements. I like to block those ads because they are annoying but they also have a big performance hit on slow hardware.
Possibly I should have asked for more details up front, including the hardware you intend to run this OS on, and in what environment, and how security savvy you are, because the older the OS, the more you need to keep in mind to use it securely. Some people who know little about security, but that are really good at just parroting something that someone else wrote, will tell you to absolutely not run any older version of windows.
I disagree with that mentality being used as a blanket statement, but I am careful to consider which vulnerabilities are relevant to my environment and needs from that system. You must do the same with whichever OS you choose, even if it is just picking the latest version of windows and letting MS incessantly update it, which personally I find to be a vulnerability in itself if you need to depend on that system always, ALWAYS working, except that can also be a reason to use newer hardware with a longer expected lifespan ahead of it, and that could exclude use of an older OS due to driver unavailability unless you have some redundancy in place, at least one other system with the same functional setup that you can switch to using if you need zero downtime.
The answer to your question can be a complex one, depending on several things that you did not mention. I could perform the functions you listed without issue on Win7 x64 (Home Premium or higher) "today" but that doesn't necessarily mean it's the best choice for you.
