I've also bought a couple old 32-bit models from e-waste recyclers who were open to me just grabbing them from out of a pile of to-be-disposed-of equipment.
Not sure where you're located, but if there is a MicroCenter nearby, the I recommend them as well. Sometimes they stock these in refurbished condition, and from my inspections of the laptops, they're in good shape. Only buy if you can look at first-hand at the store.
Sites like NewEgg, TigerDirect, and Amazon also have these, but the reviews generally don't seem favorable. One major difference is that with eBay, you can view multiple pictures of the exact laptop you will be buying. With those other sites, it's just a stock photo, and it seems like there's less quality control over what's grabbed from their warehouses.
Also it's worth mentioning that refurbished Dell Latitude and HP EliteBook laptops are comparable. There seems to be less demand for these than Lenovo ThinkPads, so often you can get better specs for the same price. In my experience, the Dell Latitude laptops have maintained greater backwards-compatibility with older docking stations. If you're into embedded development or ever want to connect to a headless server directly, then only Dell will give you that docking station with a serial port. The drawbacks is the TrackPoint on a ThinkPad is always guaranteed to be there, while it's an optional feature with Latitude and EliteBook, and even when it is there, it isn't as good as what IBM/Lenovo has engineered. Another drawback is refurbished Latitude laptops often have dedicated GPUs, which is great for Windows, but often a pain for Linux.
My 5-year-old HP ZBook's trackpoint is abysmal. I stopped trying to use it about 2 months in, and after 2 years its top surface fell off and got lost. I didn't bother ordering a replacement.
I think there is a certain inertness in perception of available choices, quality-wise. While ThinkPads were great for a time, that Nimbus should have faded by now, but it mostly didn't, although it makes no sense.
The really good ones are so old by now, that they are almost useless, except for terminal use.
The newer ones are only so, so, and the really good ones make no sense economically imo.
Then there are the mentioned alternatives. But it depends on geographic availability, time, i.e. when a large batch of refurbs enters the market, and so on. It has something of looking for flotsam on the beach :-)
Anyways, if you know hardware/what to do, then you can get great value with better options for periphery like docking stations, displays (ratio/resolution), simply more bang for the buck with about the same build quality as the ThinkPads of yore once had.
Prime expamples are small adaptors from the µSata for the 1.8" HDD to something more modern, for under 10USD a piece. Oh, and compressed air for really cleaning, new thermal grease or pads.
If you do this more often you can save insane amounts of money by getting a small compressor instead buying canned air.
Just saying...
I've had Dell Latitude machines where the hinges break after about three years and will no longer hold the screen up. I've had HP EliteBook machines where the soft rubber touchpad buttons wear through (I had one with a three-year warranty and they did fix it while it was in the warranty period.)
Meanwhile the Thinkpad machines have had no issues even after more than three years. They just look beat up (for instance there's a rubber-like coating on the lid that wears off.)
But the one that beats all of them is Apple. My MacBook Pro is now over five years old and it feels almost like new. I've never gotten this lifespan out of any Windows laptop.
I've had to upgrade the keyboard once (2-3 keys fell off), but spare parts are available on eBay, and parts are very easily replaceable with an electronics screwdriver and a YouTube video, or by acquiring the Thinkpad service manual for more advanced procedures such as upgrading or replacing your screen (Which I've done to my Thinkpad X200 running Libreboot).
We are also considering a battery upgrade, which is still available on eBay even for older models.
What’s your plan?
This isn't due to any good qualities of the sellers. It's because ThinkPad makes damn good, sturdy laptops that are quite idiot-proof. I mean if you sit on your balcony and drop your laptop off the edge - that might destroy it. But it's going to take something on that level, and most people aren't that careless with electronics.
So you can be reasonably confident that anything ThinkPad you buy, if it isn't visibly damaged in the picture, will work as expected, in my (anecdotal) experience.
If you get a high number on 1 and a checkmark on 2, it's almost guaranteed to be good for programming - realistically, for allowing you to run your browsers and something like GIMP and/or video editing.
I have a ThinkPad with 32 GB RAM and it takes a really heavy workload to pause my computer.
I frequently have several browsers & several browser windows open (say 6 windows total, mix of Chrome Brave and Firefox), and GIMP. No slowdowns noticeable (EDIT: some things do take a few seconds, like filters & exporting images from GIMP). Most importantly, using my window manager, I can switch from a full-screen browser to Emacs to GIMP instantaneously - not even a millisecond of noticeable delay.
Even many new computers purchased today can't beat that.
Also check for the screen. For quite a long time there was an Option for an abysmal 1366x768 screen. The same notebooks can be had with a proper HD screen, so get one with those.
The supervisor password is the one you care the most about.
You may get a seller who says "no BIOS password, boots up without a password." But the machine may still have a supervisor password, and if you don't have that you can't change the BIOS settings.
Always make sure there is no supervisor password, or the seller gives you the supervisor password.
Two of them had minor issues that were resolved to my satisfaction when the seller offered a partial refund of $5 or $20 (and me keeping the laptop).
All of them are still working perfectly today, including the T420 I bought for $100 in 2013 and the T400 I bought for $25 (with free shipping).
tl;dr: Ebay is a perfectly good place to buy used thinkpads. reddit.com/r/thinkpadsforsale is also good, especially if you want to buy an older one that some enthusiast already meticulously restored.