You say you’ve got PCIe 2.0 slots. If you’ve also got SATA 3.0 ports, the SATA drive is actually going to be faster than an NVMe drive in a cheap one-lane adapter (600 MB/s versus 500 MB/s). The NVMe drive only wins if you get a four-lane adapter and stick it in an x4 or larger PCIe slot, and even then, it’s only going to be about three times faster at best.

No idea about compatibility of adapters. When I was facing the same decision while upgrading an old computer, I went with the SATA drive.

I have a few of these in my 7th Gen Intel Z270 chipset machine.

Bejavr M.2 PCIe NVMe X1 Adapter… https://www.amazon.com/dp/B0CCLHQV43?ref=ppx_pop_mob_ap_share

There’s not much to the adapters, there are vertical versions like this one too, and adapters with more lanes.

JSER NGFF M-Key NVME AHCI SSD to… https://www.amazon.com/dp/B07HRLBVXB?ref=ppx_pop_mob_ap_share

I’m not sure if they’re faster than SATA3 on my machine given it’s an x1 connection but I prefer it to having enclosures hanging off USB.

I also have this to make use of the x1 slot blocked by my GPU.

XRIKUI Dual 90Degree Right Angle… https://www.amazon.com/dp/B0CBPKZ15N?ref=ppx_pop_mob_ap_share

I would just go for the SATA ones. Unless you are regularly saturating NVMe drives it’s kinda pointless, even more so for media storage. Regular SATA SSDs will do just fine and you wouldn’t have to buy and deal with PCIe adapters which just adds extra complexity and cost (slightly more expensive drives + cost of adapter)
Do also note that many of the cheaper NVMe drives generally do not perform as advertised. Since they post “up to” values. You know, down hill, urgently need to pee, sun in the back, rocket up the butt etc. etc. Depends a bit on what drive you are looking at.