Congratulations on getting a new job! I'm sort of on the same boat minus the surgery. I was working in a 5 yr contract but, there were budget cuts and 6 people from my team got cut, including me. Unfortunately for me and the others, the cuts were solely based on salaries and not performance/seniority. Long story short, my company (the contractee in the 5 year contract) offered me a severance and gave me 2 options..
1. I take the severance and I part ways
2. Because my skills and background were recognized, they offered to keep me at their headquarters helping out with their billing until they found me something or I found something myself, and I would still get the severance if I found something.
Needless to say, I took option #2 for the time being. It's been a couple of months already and of course I've been interviewing and such while working at the headquarters.
As I read your post, I figured sharing my story w/you and a little advice can't hurt. For what is worth, don't take your brother's advice this time. Quitting a job with an employer is a big no-no career wise. The saddest part of this is not the fact that, although the company may deserve it, you may need them someday for something. Ever since I started working at the age of 15, I've always left a company on good terms. Whether you worked at McDonalds or Intel, giving a 2 week notice is the professional thing to do. The world takes many turns and you never know when you're going to find yourself needing a reference. Let's say the HR manager tells you that the last thing they need to do before they send you your offer letter is check your references, right? What do you think would happen if they decide to call your current boss and and he tells the HR manager that you like to quit jobs on the spot.. Think of the "Soup Nazi" in Seinfeld calling you and saying "No job for you!"
Don't feel uncomfortable about turning in your notice. It can be a burden to tell your employer that you're leaving but, they will be alright.
Here's how you can do it:
Arrange a meeting with your supervisor. You don't have to let him/her know what you want to talk about, just let him/her know that you need to meet up with him/her. He/she may/will ask why and just let him/her know that it's related to your surgery and leave it at that, that way he/she won't know what's coming. The element of surprise is a nice thing
If you still want to F'em, you gotta do it in style and this is how you go about it... Try and schedule your meeting either first thing on a Monday morning or first thing Friday morning. The nice thing about these is that you're bound to ruin his/her day and the rest of the week if you do it on a Monday or you can screw his/her entire day and weekend if you do it on a friday.
Now, as far as the letter goes, you can pretty much get one from the net and customize it to your situation. Carry it with you to the meeting and put it somewhere where he/she won't notice it when you walk into the meeting place. As soon as he/she says "so, what did you want to discuss?" hand him/her the letter and say something like "I need to give this to you". He/she will read it and might ask you why you want to leave if they want you as an employee. Some companies will try to offer you more $ as an incentive, and if the situation was bad to begin with, they will simply accept it and move on.
Here's the interesting part...Once you hand your letter, most supervisors will completely change their behavior towards you and will treat you as if you were the new guy because you're leaving.
There's one thing for certain, you will feel like a new man once you walk out of that office.
Sorry for the long post, I hope this helps.
P.S.: Don't forget to get anything that is personal out of their systems BEFORE you hand in your letter.