Will a Lenovo W530 take a 2.5 1TB 860 EVO Sata III SSD without any issue, or do I need to buy a lower end model hard drive?

It will be compatible.
You will you need to reinstall the Operating System after intalling the new hardware.

This the laptop technical specifications

Open the back cover and find any slots. Check Crucial's website whether it has expansion.

SATA drives are all backwards compatible, so as long as the drive is the right size it will work.

If the laptop is old enough to have a SATA 2 port it might slow a modern SSD down a little, but it's not a big deal.

That will work on any PC with SATA.
SSDs make a BIG speed impact on older computers, but you are always limited by CPU…