What's the latest iOS that iPhone SEs shipped with?
The iPhone SE originally shipped with iOS 9.3. However, if you pick up a model that was manufactured more recently, it will come with a newer version of iOS preinstalled. For example, I bought an iPhone SE in early 2019 which came with iOS 10. This phenomenon is not exclusive to the SE—an iPhone 6S I bought in 2017 also came with iOS 10.
Luckily, you can use the serial number on the box of an older iOS device to predict which OS it will have preinstalled, to a reasonably high degree of accuracy. Just enter the specified digits of the serial number on this website: https://repo.bearlike.net. Note that for newer devices, Apple has announced they will transition to randomized serial numbers in mid-2020.
Unfortunately, you're going to run into a different problem after acquiring a device. According to an FAQ in the Jailbreak subreddit (Jailbreakers have reason to keep track of these things!), as of this writing Apple's servers will refuse to activate an iPhone 6S, iPhone 6S+ or iPad Air 2 that's running iOS 9.
You might have more luck with an iPhone 6 or iPhone 5S. These devices aren't listed in the FAQ, which could mean that they work, but could also mean that no one has tried them and documented the result.
The other option is to buy a device that can't be upgraded past iOS 9, although as I'm sure you're aware, these models will run more slowly.
Lastly, the checkm8 exploit may eventually allow iPhone X and older devices to be downgraded to any compatible iOS version. However, no one has actually built software to do it as of this writing. And, any future tool that does will break touch ID, and require you to connect to your computer in order to boot your phone.
While the iPhone SE originally shipped with iOS 9.3, you'd most likely not find find a recently manufactured one coming pre-installed with iOS 9.3 (or a later version of iOS 9.x).
iPhone SE models was discontinued on March 21, 2017 (16 and 64 GB variants) and September 12, 2018 (32 and 128 GB variants). Either one of these models, which you'd most likely find with a reseller who is still selling them, would most likely come pre-installed with either iOS 10 or later (but still below iOS 13).
If iOS 9.x is what you are looking for to access iOS 9 exclusive apps, here's the list of iOS devices that can't be upgraded past iOS 9.x. Getting access to one of them could serve your purpose:
iPhone 4S (latest operating system: iOS 9.3.6).
iPod Touch 5th generation (latest operating system: iOS 9.3.5).
iPad 2 (latest operating system: iOS 9.3.6 (Wi-Fi + cellular (CDMA)), iOS 9.3.5 (Wi-Fi and Wi-Fi + cellular (GSM))).
iPad 3rd generation (latest operating system: iOS 9.3.6 (Wi-Fi + cellular), iOS 9.3.5 (Wi-Fi).
iPad mini (latest operating system: iOS 9.3.6 (Wi-Fi + cellular), iOS 9.3.5 (Wi-Fi).
Source: List of iOS devices