Remove Employer/Job Title Fields and Reorder Fields
You can adjust the order of the panels under Display Preferences here: civicrm/admin/setting/preferences/display?reset=1

The order of your custom data sets will be based on the order of your Custom Data here: civicrm/admin/custom/group?reset=1

Under display preferences you can also hide some fields, but not the ones you're after. We never customize our installations to remove those types of fields. Unless you have the skills in house for those types of customizations, you may end up relying on a developer for each upgrade to hide them every time. Most find that an unnecessary expense and just ignore them.

Heather.