The longer straps are called the Shopping version, but I stand to be corrected.
You get LH (long handle) and SH (short handle) . Then you need to decide which size you want to go for. They come in small, medium and large. If you buy preloved, the sizes could be a bit different as they changed the sizings of them some years back. The small then, is what a medium size is now. My dd also just got a fairly old size medium, and its very similar size to the new large.
Some of them come with a crossbody strap as well now though, so you could look at those.
The printed jockey logo is legit. I think this is the green (as in eco) range.
If you are buying 2nd hand, scrutinize the photos. You can look on YT as well for how to spot a fake. Some are quite good fakes, but you can usually tell by looking at the stitching, the leather flap on the front, the leather should be in a diamond pattern. And then the name of the back in the leather, if its very pronounced, it can be a sign of a fake.
I have bought preloved and the downside to that is that if the previous owner has had the corners re-stitched (they are notorious for fraying on the corners), then the bag will be slightly smaller than it was originally. As they re-stitch the whole seam inside.
They hold a ridiculous amount of stuff. I noticed my dd's one started to bubble slightly, so I steamed it. Then I thought I would fill it with rolled up towels so it keeps its shape until it was properly dry. I stopped at 8 rolled up towels, and I reckon I could have put more in there (but the linen cupboard was pretty bare at that point). I was laughing doing it as it just would not fill up 😀
If you can find a Neo I would be tempted. They are now discontinued. They are a bit thicker in the fabric and they tend to last a bit longer. But they don't fold up as they don't have the popper on the back.