If you've got the OEM ball joint/trunion combination (haven't yet re-built it and replaced it with the greaseable Spicer equivalent), then you'll want to get a syringe tip for your grease gun to be able to get enough grease into the ball joint to get the needle bearings lubed up.
The stock ball joint and trunion (at least on my '98) was a "sealed" (yeah, right) unit, so after a little water/snow incursion the needle bearings were washed clean of grease, dried, rusted up and turned to dust - resulted in an annoying sqeaking, and finally a clunk as the trunion began to wear down. It's inevitable that this'll happen eventually if you wheel your truck....the OEM unit is not meant to last.
Yes, the conical fitting is the one that you'll need for the recessed grease fittings (if you have 'em).
If you take the driveshaft off the vehicle you can manipulate the double cardan to be able to get at the grease points, and to spread the grease around. Doing it on the truck is well-nigh impossible. I take mine off twice a year to get all the old watery grease out - though still will grease the accessible fittings at the regular intervals with the shaft on the truck.