Will a ticket for following too closely which is two points or a ticket for careless operation which is zero of a vehicle affect my insurance more?

A lot depends on where the ticket is from and where you are licensed to drive.  For example, if you are licensed in South Carolina but the ticket is from another state, that would be one scenario.  If you are licensed in another state and the ticket was in South Carolina, that is another scenario.  The first thing I can tell you is that other states have all sorts of odd ways to handle tickets and South Carolina has none of those.  I get a lot of questions from NC drivers about "plea for judgment", "conditional discharge" and other things that supposedly NC has.  SC has none of those so if you hear something from a driver in another state, do not let it fool you into thinking the same thing is available in SC.

In SC, some cities or counties have a special ordinance called Careless Operation (also "Disregard of Traffic Laws" and other names).  The reason it is no points is because the state does not acknowledge that as an offense. This means that a state trooper cannot write that ticket but only a deputy or city policeman can.  HOWEVER (big letters), just having the ticket changed to that is not a guarantee you will avoid any points on your license.  If you get that charge and are licensed in another state, I am told by many callers and clerk of courts that other states will often pick up the offense (because it will be on your driving history) and some treat it as Careless Driving (6 points or immediate loss of license in some places).  Are you willing to risk that?  Even the states that do not treat it wrong still treat it as a 2 point violation so all the work to avoid the points ends up being no use and more often than not, it causes a snag in your home state that you will be spending years trying to straighten out.

If you are a SC driver and the ticket was in SC, the Careless Operation offense can keep points off your license but many insurance companies are wise to that.  Of course none will raise your rates, you just lose your discount (which is the exact same thing but they love to play with words).  Many do not raise your rates for the first 2 point violation but you would have to check with your company.  This also alerts them to check your driving history though.  Often, they do not check your driving history at every renewal.  It is entirely possible you could have the 2 points on your license and they would never notice it at all until they have come off of your license.  So, getting the information you need from your insurance company could also give you a bigger risk of them realizing to run your history and thereby raise your rates (take away your discounts, whatever).

Best advice is to be careful and remember that most insurance companies will claim not to raise your rates for almost anything you do since they phrase it as a denial of a discount rather than a rate increase.  Also bear in mind that if the ticket was from a state trooper, it cannot be changed to Careless Operation (or whatever that municipality may call it).  If you from out of state, take the 2 points and play it safe.  If you are from in state and the ticket was in state, I would normally seek the Careless Operation if I could get it.  One final note is that how you behaved with the arresting officer can have a big influence too since if the officer does not wish to change it to Careless Operation, it will not be changed.

Hope that answered your question.