Should I register to vote to get picked for jury duty faster? ?

Each state has a different method of picking potential jurors.  For some, it is indeed the voters list.  For others, it's the DMV list.  Still others have a combination of lists, including real estate records, they use.  You can check for your state online to determine how they compile their list.

You can if you want.

All you need is a driver's license to get called up for jury duty, but you should register to vote anyway.

In my state, they get the Jurors names from your driver's license.

I can directly verify that voting registration is the primary way pools of potential jurors are selected for jury duty. 100% of the people I have helped to secure driver's licenses and register to vote, (through the DMV), got called not long after and they had never been summoned before despite having longstanding permanent addresses.

These were people who got help from a nonprofit organization I was working with to help them get driver's licenses to assist in getting to their new jobs and register to vote, (if they wanted to). Those that didn't register to vote but got their licenses anyway were never summoned. That cannot be a coincidence. 

That is why I think it will be hilarious when many of the 'new' Biden voters get called for jury duty and never show up because they don't exist.

Registering to vote will not get you picked any faster for jury duty.