Buying a used iMac for data restoration and OS compatibility

The essential requirement is for that Mac to have been correctly prepared for sale according to What to do before you sell, give away, trade in, or recycle your Mac - Apple Support. Those instructions must be complied with, ideally under your direct supervision.

Removing its firmware password is also a requirement: What is a firmware password on Mac? - Apple Support

If any part of those instructions are not fully complied with, then you will have bought a useless "brick".

... if I was running an older operating system than a new iMac for example?

That will not be a factor because you will be restoring it from your "dead" iMac's Time Machine backup. That will restore everything including its operating system.

Confirm that Mac is configured with internal storage of capacity equal to or greater than yours. The only options for that model were a 1 or 2 TB HDD or a paltry 256 GB SSD. No matter which, if it is the iMac's original storage be advised they have already reached their end of expected service life. If it has been upgraded, investigate.

That Mac's GPU has also been afflicted by a limited service life due to its life-limited internal flash storage. No replacements are available.

If it is not already abundantly clear, buying a Mac of any age is best left for very experienced Mac users. Buying one that old is so unattractive that experienced users won't be interested, unless it's free, in which case it would be best suited for installing Linux Mint, not an antiquated macOS version. High Sierra (the latest that one is capable of) is about to lose its security certificates as they are due to expire in a few short months. That means the software you presumably wish to keep using will not be an option anyway.

Nobody likes to keep older Macs in service more than I do, but a fifteen year old model, even if its hardware is 100% perfect (which it won't be), is certain to be a frustrating experience at best.

You did not ask for my opinion but if you did it would be "don't do it."

FYI, there are several things working against keeping an iMac that is as old as yours (iMac (27-inch, Mid 2011)) or mine (iMac (27-inch, Late 2009)) going.

For both of those iMacs, High Sierra is the end of the line.

• High Sierra is not enough to run current commercial software, or even current versions of open source software such as Firefox, LibreOffice, the GNU Image Processing Program, etc. Firefox 115 ESR will run on High Sierra – and has gotten many "stays of execution" with regards to the end of "critical security update" support, but even relying on it may be "hanging on by your fingernails". You can get old, unsupported versions of LibreOffice that will run on High Sierra, but where photo editors are concerned, GraphicConverter 12 might be the only major one left standing.
• Apple recently raised the minimum requirements for accessing iCloud. A few weeks ago, you needed High Sierra or later. Now you need Mojave or later, which locks out Macs that cannot update past High Sierra.
• As far as any of us know, High Sierra will not be getting the security certificate update needed for iMessages and FaceTime to work after next January. I haven't heard of Mojave getting the patch, either, although maybe it will, if Apple decided to raise the minimum iCloud requirement to Mojave rather than to Catalina.

If you're trying to keep old one-time-purchase Adobe or Microsoft applications running – applications encumbered by activation DRM – you may discover that the activation servers have been PERMANENTLY taken off line – leaving you with no way to move your purchased software from one old Mac (that failed) to another (that hasn't failed yet).

One of these old Macs might still be useful for running old 32-bit games (unless App Store / iCloud changes cause DRM on those to break, too), or for importing digital video from MiniDV and Digital8 camcorders. A 27" Late 2009 one can be booted into Snow Leopard to run some Mac/PowerPC applications (e.g.,, games) under Rosetta 1. And Linux might run tolerably well on one of these machines, if it is in working condition.

Depending on the 3rd party software you use, newer macOS versions might not support this software anymore and you might have to buy the software new.

Have a look at the list of compatible Macs and macOS versions:

...

Find out which computers are compatible with the most recent versions of macOS:

• macOS 27 Golden Gate is compatible with these computers
• macOS Tahoe 26 is compatible with these computers
• macOS Sequoia 15 is compatible with these computers
• macOS Sonoma 14 is compatible with these computers
• macOS Ventura 13 is compatible with these computers
• macOS Monterey 12 is compatible with these computers
• macOS Big Sur 11 is compatible with these computers
• macOS Catalina 10.15 is compatible with these computers

...

copied from: How to download and install macOS - Apple Support

You're getting a lot of great advice here. One I would like to add a bit to, is the one from Old Toad.

FWIW, I have been using the Mac mini series since its Early 2006 model. I upgrade them every 3-5 years, and currently have a 2023 M2 Pro mini. Being that it's still a bit early for my next upgrade, I most surreally will be continuing that trend into the future. The bottom line? I have never been disappointed with any of them. They have also never failed me. Having the option to choose my own monitors, keyboards, & mice was the selling point for me.

If going used is your preference, then two great sources are: 1. Apple Refurbished, & 2. OWC. My only suggestion is be aware, in case you didn't know already, that Apple only supports the last three versions of macOS. Currently that is Golden Gate, Tahoe, & Sequoia. I would aim for a mini that can support, at least, Sequoia, if not Golden Gate. For example, the 2018 mini can support Sequoia ... but not Tahoe or Golden Gate. It is also the last Intel CPU model. However, note that it is at the "end-of-the-line" for macOS. All the Silicon (M1-M6) models can support Golden Gate.

You’re headed for a transition to Apple silicon too, which means older apps will need upgrades or replacements, as the two have very different internal architectures. Intel apps are last supported with macOS 27.

Or you’re headed for building up a stock of spare parts or spare Macs and the rest, and either learning how to maintain your own hardware, or having the budget for somebody else able and willing to maintain it for you.

Staying behind is cheaper, right up until it’s not, and then it usually gets expensive faster. And the further back you allow your data to get, the higher cost of getting to current apps.

If your most important apps happen to use deprecated data formats, you can need custom tools or even custom reverse-engineering and development work to get that data preserved and updated to current. There are old photo media-storage formats that just don’t exist any more, and tooling is scarce and expensive.

Vanishingly few computers are truly isolated things anymore. Most computers now exist and operate in networks, and the rest of the network and its operational and security requirements invariably drags apps and operating systems forward. This beyond managing what is inevitably-degrading and inevitably-failing hardware.

Even hammers degrade, and get repaired or replaced. And hammers are way less complicated. And not networked.

Unless you can confirm that the used Mac has been prepared according to the Apple document that John Galt referenced you may be in to an expensive door stop.

If budget is a concern (or not) consider a new Mac Mini as follows: a 12‑core CPU, 12‑core GPU Dual 16‑core Neural Engine Mac Mini M6 with 16 GB RAM and 1 TB SSD ($1399 US) with a 32" LG 4k monitor ($331 US) from Amazon.com)  is $1716 which is $480 less than a similarly configured new 24" M4 iMac ($2199 US). Keep your keyboard and mouse from your current Mac for use with the Mini. If you recycle don't include the mouse an keyboard.

I got the previous Mini M4 with a 32" LG 4K monitor w/speakers for the same price as a 27" monitor (didn't know the Mini had a speaker).  There are many monitors available in 27" size for about $100 US to $500 US depending on what features you want.  I love the extra screen real estate of the 32" monitor.

I had an 2017 i7 iMac with an SSD boot drive and a new M4 Mini runs circles around it.  The new M6 will be even faster.   

You can use the keyboard and mouse from your current iMac. Don't include them with the iMac if you use Apple Trade In or recycle with the  iMac.

With this machine you'll be getting the latest Mac and support (both madOX, fixes and security updates) for several years to come.

Just some food for thought.