I agree with Juanita in that if you are unable to work full time applying for unemployment will not help you because it is a short term solution.
You should apply for SSD. I did this when I was diagnosed in 2009. You apply on line and they will call you to verify the information. It is very important to hire a lawyer who has experience in SSD. I was lucky in that my boss had a very good lawyer who I had a good relationship with and I knew that he didn't handle SSD cases but he would direct me to a competent lawyer. Once the social security administration issued a claim number for my case, my lawyer sent a form to me to have my neuro fill out comfirming my condition. The lawyer sent this form along with a letter comfirming my diagnosis. It took about 30 to 45 days to hear back from the social security admin. and during that time my lawyer was ready to write another letter saying that if they denied my claim we were ready to appeal.
I was approved and they were going to start my benefits back to June 30 when I lost my job even thought I had started the process in November. Also they will decide whether you have to "reapply" in a period of 3 or 7 years depending on the severity of your illness. I was given a 7 year reassessment period. It is true that the government sets the amount your lawyer will receive and it is a percentage of the initial amount you receive.
I'm lucky that the process was so easy but I believe that having a good lawyer helped tremendously. Good luck with your journey.
Southern Bell