We are currently using SP2013 with many custom lists. I have been using JQUERY to build them.
My question is what is my options to rebuild the lists in SharePoint online?
Can I use JQUERY again?
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If you are going to use classic experience in SharePoint Online, you can still use JQUERY & custom scripts in team sites.
If you are going to use the modern experience:
For list form customizations: You can use Power Apps customized forms, conditional formula to show/hide fields, JSON to format the list forms
For list view customizations: You can use column & view formatting with JSON Or SPFx extensions
If you need to develop any complex solution in SharePoint online modern experience then you have to use SPFx web parts.