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.