This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
as you said you have very limited experience in JEE , then i recommend you start with OCEWCD i.e web component developer exam. this will help you in other certifications as well for example EJB. it does not mean that you cannot do EJB certificiation right away after OCPJP but as moderators say all the frameworks like EJB , struts, spring have there base in servlet and jsp so it is better starting from the base and then moving it up. once you have done OCEWCD then you can either go for EJB or for web services.