My approach is similar to Scott and Troy in terms of the stem's interference fit but I just wanted to add that I like to blunt the end of the stem with a diamond file before pressing it in. Just a little extra insurance to discourage it from hammering through the poppet. I haven't managed to rupture one yet and I'm not enough of a masochist to deliberately insert a sharpened stem for the learnin', so I don't really know how much the blunting helps but it sure doesn't seem to hurt.
And since we are on the topic of making a reliable, long-lasting poppet, the other thing I wanted to comment on is the sealing margin on the poppet's OD. In other words, how much overlap onto the valve throat do you need to ensure the material will not extrude over time? This will take a couple of paragraphs to explain and work through an example but after you've done it once, you'll realize it's actually quite simple.
The compressive strength of PEEK is typically about 15,000psi which means we want to stay well under that. I like to expose a poppet to only about half that much on account of there being a dynamic element to the poppet snapping closed [see footnote 1 below].
But how how do we figure how much load it's seeing? Well, we first look at the force holding the poppet closed. That force is calculated as the throat area times the operating pressure. So let's put some numbers to it...let's say we have a 0.230" throat and running at a regulated pressure of 2000psi. The area of a circle is pi * radius squared. So a 0.230" dia circle has an area of pi * 0.115^2 = 0.0415in^2. 2000psi operating against 0.0415 sq. in. is 2000*0.0415 = 83lbs.
So we have 83lbs of force squeezing the poppet closed. Our poppet is a circle that overlaps the throat by some small amount. Meaning this 83lbs is supported by just the rim of the poppet. Let's take a stab at it and guess that maybe a 0.020" overlap might be adequate. Twenty thou ain't much but let's see. This 0.020" overlap on the radius doubles to 0.040" in terms of the poppet's diameter, meaning our poppet is the 0.230" throat plus 0.040" = 0.270" dia. The area of this poppet is therefore pi * 0.135^2 = 0.0573in^2. Subtract the throat area of 0.0415in^2 and we have a rim of 0.0157in^2 supporting the 83lbs of force. So the load on the PEEK material is 83 / 0.0157 = 5300psi. 5300psi is well under PEEK's 15000psi rating and also under my preferred "half of 15000psi". So you might consider going a little more aggressive and reduce the poppet a few thousandths but unless you have good reason to think it will help with the valve's flow characteristics, that would probably represent a high risk/low reward scenario.
All of this was for a flat valve seat so you can think of it as a worst-case. Meaning if you go with a conical seat, I think there is an angled wedging component to the force acting on the poppet that would tolerate a slightly smaller sealing margin. But again, in most cases there is no compelling reason to shave down the sealing margin to the razor's edge of what is reliable.
[1] some discussion on that topic
https://www.gatewaytoairguns.org/GTA/index.php?topic=180328
