Fastest would be the shuttle bus
Click on Shopping Express button with the grey background above the map.
EUR 20 pp, children up to 12y free
Cheaper and more flexible would be the trip on a Bayern Ticket (Bavaria Ticket).
EUR 31 for 2 persons together, children up to 14y free
From: München Hbf (or wherever in Munich you stay)
and select "only local transport".
Bayern Ticket covers the regional trains between both cities. And all other local public transport in Munich and Ingolstadt.
Ingolstadt is a nice city and also the Audi Forum is worth a visit.
Many thanks, great info !