I am first timer and I was wondering if having an account with any of the screening sites is a plus, if they help speeding up the screening process for providers dealing with a first timer.  

Which of P411, RS2000 is the better choice?

because providers rely on them.  Of course, they may also require addtional screening for a newbie. P411 also lists providers who are "newbie friendly," so you can find ones most likely to see you.  I understand RS2000 is mainly a midwest service, so if you're in Chicago, for example, it might be a good choice.  But P411 is more national, as is Date-Check.

a screened client is a happy client by being on screening websites, it helps eliminate the extensive process of applying toto each individual providers light to heavy screening by being on these websites, I can't garantee that it will eliminate all of screening but it does definitely give you an advantage in the long run and help to build reputation faster.