The answer is that no only is everyone different, but every surgery is different and every anestheiologist is different.
I have had multiple surgeries. My waking up experience has been different with each. Some were horrible and I was vomiting and confused and dizzy. Some it took me hours longer to wake up in recovery then normal. Some were great and I while I was groggy I felt okay pretty quickly. Some I go home and sleep for about 2 days. The last one I was home watching TV, eating meals and socializing with my family and felt great.
Until you go under for the first time you really don't know. I now know to tell them that I am very likely to vomit and that I don't wake up easily so they adjust the meds they give me accordingly, and that is why my last few experiences have been much better.
As for pain that is all dependent on what they are giving you in your IV, if they gave you a local anesthetic in surgery that will remain in place for hours, and your overall pain tolerance. Certainly Lap procedures are much easier to deal with than larger cuts but you still will be sore and uncomfortable.
I also think that the anticipation of what may happen has always been much worse than the actual! If you are really anxious when you get to the hospital they can give you something to calm you down once the IV is in. I find that very helpful because otherwise I am likely to try to jump off the bed as they are wheeling me to surgery!
Best of luck for a great outcome!
ETA: Ask your doctor if they will be filling your abdominal with gas during the procedure. Not sure if they do for that procedure but I think they do for many lap surgeries to get room to see and work. That can be very painful for a few days if they do. After I had my Gallbladder out that hurt worse than the surgery areas! You can help by walking and raising your arms and using heating pads-- the pain is usually in your shoulders.