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.
If you have no preferences to go by, start with the SCBCD. It has already been upgraded to cover recent JEE APIs. The current SCDJWS exam is partly based on obsolete APIs that have already been removed from JEE.
Market research : check the job skills required for positions on your LOCAL web site. The skills in demand in the US on Dice.com may not be the same as on Jobserve.com.au. Some skills are impossible to learn home alone (server Admistrator). You must have hands on experience. Other replies are , I think, promoting their own skill set or just repeating the path they followed. I migrated from IBM mainframe to Oracle client server - code is just a grind but screen development (in my case Forms) even though intellectually simple is very difficult without a good example of 'look and feel' (which I did not have). I'm staying server-side.