A needle is repeatedly jabbed into your skin so its uncomfortable but not severe pain. The feeling is more like a burning sensation. The smaller the size the faster it will be finished. Just go to someone that can take their time and stop occasionally if need be. Something like you mentioned would probably take 15-20 minutes to complete.
If you have less fatty tissue around your wrist then it means that you might likely experience a bit of pain in getting a wrist tattoo, as compared as getting a tattoo on another part of your body. This is because fatty tissue tends to protect the nerve endings and also assists to minimize pain.
Inner wrist is a lot more painful since you have very thin skin and you have arteries and veins exposed. Outer wrist has a little more tissue, but it's right on top of a bone. I have 5 tats but I put them all in places that can be hidden for work or shown in regular clothes. All depends on what type of job u have