If you want a formal wedding, then everything should be formal. This way your guests understand that and dress and act accordingly on your wedding day.
Once you say “YES!” then of course you (the bride & groom) call your parents and siblings and spread the news. You’ll want to bust and tell everyone and that is OK but your next step is to create that guest list and send announcements – “We are getting married!” these don’t need a date and they don’t have to be fancy, but they should be formal with a little personality in them.
Of course everyone wants their photo in the newspaper so I would do that next then start planning! Until you know approximately who is attending finding a venue doesn’t help if you want 300 people and your venue only fits 100.
Then comes save the dates and invitations of course. With a formal wedding it is best to take your time and plan, don’t rush. Also having a formal event doesn’t mean that it is an expensive event.