There is a LOT of info here to get you started on your search for info.
Some things that I've run across in my years of research and talking with folks... Thyroid Cancer, if you have to have cancer, is one of the easier ones. That's not to say that I minimize it... but... well...
I'm not a doc... don't use the REALLY big words... just share what I've learned.
Thyroid cancer tends to be very localized and removal of the gland pretty much removes the cancer. Then, with proper hormone replacement, it's not likely to come back at all... there are exceptions to the rule... but the chances are small.
The key, the VERY important key, is how you handle things after.
To keep any remaining tissue from causing a ruckus you need to take enough replacement hormone to suppress the TSH levels. By doing that the tissue won't be trying to recover, grow, produce hormone and stimulate a return of the cancer.
Proper levels of the active thyroid hormones (Free T4, and Free T3) will mean that the body isn't sensing a need for more hormone and the Pituitary Gland won't be producing TSH to signal the thyroid gland to produce more hormone.
To put it in really simple terms... Getting the correct tests done to determine thyroid hormone levels will assure you that you are getting correct dosage to suppress TSH and keep the remaining tissue asleep.
Simply testing TSH will NOT accomplish this.
I keep referring to remaining tissue... that's because the thyroid gland is so very very delicate that they can not remove every last bit of the tissue during surgery, there is always a small amount left behind.... So it's up to you to understand that, and to make sure that your doc understands that, and to make sure that your replacement dose of thyroid hormone is the correct one for YOUR body and to keep your TSH suppressed AND your thyroid hormone levels were they need to be to allow you to be healthy.
With proper medication you can live without a thyroid gland. Having it removed is not a death sentence. Education, understanding thyroid function, hormones and replacement dosages will make this easier to deal with.