You should consult a competent local business attorney wth experience in the area of non-competes. In general, they are enforceable if reasonable in geographic scope and time, depending on your particular industry. If you are an at will employee, since you are already working, in most states there would have to be some additional compensation, or "consideration" to make the non-compete contract enforceable.
Continued employment is valid consideration for a non-compete agreement in Florida. I think that's terrible, but our legislature has so far allowed employers to fire employees for refusing to sign. If you think it's wrong, talk to your state representative and state senator about changing the law.
I'd suggest having an employment attorney review the contract for you so you understand your rights and obligations before you sign. You may be giving up too much to make it worth signing. If the employer wants you to stay badly enough they might be willing to negotiate the terms. But you may have to decide that it's time to move on to another employer. Of course, the new employer can wait until you start, then demand you sign a non-compete too.
Issues you need to be concerned about include what happens to the book of business you brought with you, how long and what geographic areas the restrictions encompass, is your employer's actual business accurately defined or is it overbroad, and if you're a creative person (software designer, writer, painter) are they going to try to make a grab for non-work related creative works you do on your own time while you're still employed.
I hope this helps.