A couple things to add to the above:
Rule of thumb is one to 1-1/2 pin diameter out each side, excess length before peining. So, if total thickness of tang and bolsters adds up to 1/2", and you are using 1/16" pin stock, cut your pins 5/8" - 11/16" in length. Less, and the pins won't have enough to form a head before getting too short. More, and they will tend to bend and otherwise fail.
I find it helps to use a light ball pein hammer. I start the peining by very lightly forming a symmetrical head with the ball pein, then gradually upsetting it until the pins won't move anymore, flipping the assembly over as needed. When the pins begin to tighten, I switch to the flat face of the hammer, and hit the pin heads harder, finishing with pretty forceful blows. I feel that this helps the metal upset in thickness into the bolster stock, fitting tighter and greatly lessening the possibility of seeing the pins when ground and polished. Starting lightly with the ball end also helps the pins not to bend before they form a head and tighten up.
After hammering the pins tight/flat, I often go and squeeze the assembly in the post vise, with spacers to avoid the pins and concentrate force on the actual bolsters, to further tighten the bolsters and squeeze out epoxy, and then go back to the anvil for a few more hammer blows on the pin heads.
If you don't want to see the pins when the knife is done, try also not to get any epoxy on the pins when pushing them through. Glue only the bolster/tang joint. If the pin stock seems very surface oxidized, sanding the stock lightly with 600-ish before cutting it may also help to avoid visible pins. And as mentioned above, try when possible to use the same alloy for pins/bolsters. Nickel silvers have differing alloy quantities too, sometimes.
Lastly, I'd start with nickel silver to learn on. It's easier than stainless to work with. Just my $.02.