Not a great time to be buying drives or memory because AI needs are driving prices up, but it doesn't seem like that's going to change anytime soon, so it is what it is.
Your first decision needs to be whether to go with SSD or the legacy spinning HDD. It will cost a bit more per GB, but I think a SSD is very much worth the cost. Yeah, everybody conceptually accepts SSDs are faster, but many may not appreciate by how much. For a side-by-side illustration, see my video:
"Demonstration of SSD Booting Speed vs HDD"
My video compares a M.2 SSD, which is a tad faster than the 2.5" SATA form factor you'll be looking for, but it still gives you a good idea of how a traditional HDD compares.
There are lots of different SSD form factors, but you want to look for one that is the same 2.5" form factor and is a drop-in replacement for a traditional laptop HDD.
FTR, my wife still uses a 3521, which I upgraded with a SSD a few years back. It still works well for her. She uses it mostly for zoom meetings, sonce the laptop has a camera while her desktop rig does not.
As for size, 250-500 GB should be enough if you're price conscious.
As for brand, I prefer to stick with the well-known brands like Samsung, Western Digital, Seagate, Kingston, or Sandisk. As a PC tech I used to buy lots of drives to upgrade clients' systems, but I've been retired for several years so my brand preferences may be old prejudices talking, so take that into consideration.
I'd stay away from the lesser known brands because there are a lot of fakes flooding the market these days. For the same reason, I also stick to reputable vendors like Newegg.com and "Sold by Amazon". Avoid the third-party resellers on Amazon, Newegg marketplace, eBay, and the like. It's just too easy to get scammed.