Identify the market for your new series - does it really exist?
Understand all of the costs to run the series including what a realistic "average" cost for competitors would be.
Understand what income might be from entries and ideally series sponsors.
Work out the technical / sporting regulations for the series - to make it "budget" it has to prohibit just about all car modifications.
Work out a plan to launch and promote the series and to run the series for the next few years.
Register it all with the MSA (if running under their jurisdiction)
As I suspect you will not necessarily be looking to become an organising club you'll need to find one that you can run your series through
Bottom line though is before diving in make sure there really is a sustainable market that will deliver reasonable grid numbers on a regular basis .... ideally without getting into a turf war with existing series/championships. We already have more than enough "small grid / catering for similar markets / we want our own version" series/championships
.