W2 employee contract

Umm, I live in Virgina and I am fairly sure that employees don't pay unemployment insurance.  Only the employer does.  I know that I have never see any deductions for it specifically on my pay-stub.

I will agree that the W2-contractor is a myth.  I have never seen a real contractor fill out a W2.  Part-time, yes.  Not even sure about a temporary employee, the only temporary employees I have used were though firms that specialized in temp  and temp-perm placements.  I paid the firm and the firm paid the employee.

Now, some places require you to sign a contract of employment, which is different from being a contractor.  You are a regular full-time employee however the company can choose not to renew your contract and the end of it term.  Although this sounds like a contractor, it is legally different.

I know I worked for a public school system that worked that way and I had a normal W2.

in this case after signing a contract and working as W2 employee, if I find another job I can quit with no notice and it will have no downside on me.

That depends on what is stated in the contract and what your state laws are.  Also, just in case somebody who is in that situation reads this, it also beleive it depends on if you are a US citizen (or have a green card) or you are a H1B Visa holder.  I don't think H1B Visa holder can just quit one job and go to another one.

Example:  Where I currently work all of your vacation that you accrue is available for you to use on Jan. 1.  A new employee gets two weeks a year.  So say you started on Jan. 1, you have two weeks you can use on day one, but you have not earned them yet.  So on June 21 you took two weeks off.  Then you came in and quit the day you got back from vacation.  Well you have only worked for the company for 6 months, so you have only earned 1 week of vacation and you took two. You owe the company money for the other week of vacation that you took, but had not earned yet.

As you can see nothing is simple.

Even if you signed a contract, some state laws give employees "Rights" which means that you can't be asked to sign them away.

So, (in many places) even if your employer claims that you can't get unemployment benifits, you still can.  And I don't think there are any states where you can sign away worker's compensation rights.  (That is on the job injury insurance.)

Again this appliws to folks who use w2 rather than 1099.  

Folks using a 1099 are truly contractors and are not covered by the normal employee protections.  Of course there are exceptions, and many employers break the law by using 1099 when the law states they should be using w2.  That is where we get to the myth of w2 contractor...