So, I've used many different Surface Pro generations. In theory, all the latest active pens are supposed to be compatible with the 4. In practice, though, that's not actually the case - they improved the technology for the 5, and the pens are less backwards-compatible.

You'll need something that explicitly says it's compatible with the 4. Something like this: www.ebay.com/itm/292527539912

I've used that exact pen on my 4. Worked fine for me.

The safest bet is to use an OEM Surface Pro 4 pen, like this: www.ebay.com/itm/800081248150

The SP4 pen has one side button and a pocket loop.

Don't get any pens that say they work with 5 or later. They may or may not work on your 4.

Avoid the SP3 pen (two side buttons) because it needs an extra set of button cell batteries. It's kind of a pain.

You'll need a AAAA (quad-A) battery. Those things may cost more than you'd expect, because they aren't very common. Pens with rechargeable batteries are much newer, so you're unlikely to find one that works with the 4.

I hope this helps!