I am more of a section walker but am planning to extend the via francigena (I have done half of it which is England to Rome) to eventually reach Jerusalem. There are several posts on this forum so worth searching for them. There is also a Facebook group of a confraternity of pilgrims to Jerusalem.
There is also a website on the Jerusalem way
JERUSALEMWEG / JERUSALEM WAY: The pilgrimage route to Jerusalem is the longest peace route and international cultural route
www.jerusalemway.org
Heading to Jerusalem is more complicated as you read people's experiences, and at some point will probably involve taking a flight no matter which route you take due to issues in Syria or lack of ferry routes for crossings in the Mediterranean. It would be a tough pilgrimage and guessing from your name, that like me you are female, which may raise further issues depending on route taken to Jerusalem.
Not to dissuade you from Jerusalem, but some of the European network of camino routes may be "easier" to plan. And as I am a fan of the via francigena it would be possible to do it then follow a camino route from Italy to SdeC. That is the glorious nature of the network of pilgrimage routes in Europe, it provides many options!