I'm so glad that you asked me instead of getting your guidance from magazines and websites that are primarily concerned about making the advertisers happy, not with telling brides the truth. You don't send 'save the dates' at all. If Jeremy and Jane are so dear to your father that he wants them at your wedding, then your father can take pen in hand (or grab his cell phone) and write a short personal letter (or send an email) to Jeremy and Jane. Ditto for the groom's mother informing her own family, and you informing your personal friends.
The key word here is personal, meaning uniquely created for the recipient, not some identical 'spam' going out to everyone. Communication via impersonal mass produced junk mail is for commercial enterprises like dental offices and pizza parlors. This shabby sort of communication is not at all good enough for special social events like your wedding.
Since the messages will be coming from several different people, it is those several different people who choose their stationery -- or choose to send a fax or smoke signals or whatever. If you want to use matching stationery for your own letters to your friends, that sounds charming.
You mailing dated depends when you need your exact head count so that you can finish your seating chart and inform the catering firm. Mail on that date minus 10 weeks. A week after the mailing, put your helpers to work contacting everyone who has not yet contacted you. Miss Manners tells us that when we receive an invitation, we should promptly acknowledge that invitation. If we are not sure whether we will attend, we ask "May I have until the end of the month to respond?" (Acknowledge means "I got the invitation." Respond means "I will [or will not] attend.) So it is not at all "pushy" for your helpers to phone people and kindly inquire whether the postal service has delivered the invitation.
This polite prompt to acknowledge the invitation is followed by an equally polite "May I tell the couple when to expect your response?" If people ask for a deadline, the answer is "As soon as possible. Will you know by next week?" Give people a weekly reminder here, not permission to dawdle until the day before the deadline.
You may have noted that RSVP cards are not a part of this RSVP process. Response cards are yet another invention of magazines and websites that are primarily concerned about making the advertisers happy, not with telling brides the truth. Put a phone number right on the invitation, just beneath the letters RSVP. As stated earlier, your helpers take and make most of the calls. Indeed, this used to be the cheif duty of bridesmaids and groomsmen, back before bridal magazines and websites decreed that their cheif duty is to be cash cows, buying scads of merchandise for numerous extra parties.
Make sure your helpers are prepared to fill in the details that are not included in your crisp elegant invitations.
How dressed up should I get?
What's for dinner?
Will there be booze?
and last but not least "What kind of gift would the couple most appreciate?"
Also make sure that your helpers are prepared to say things like "There is a misunderstanding. The invitation is for Mama Bear, Papa Bear, and Baby Bear only. Goldilocks is not on the guest list." and "The couple would like to be able to welcome everyone, but I'm afraid the wedding will be limited people that the family knows and cares about."
I hope this was helpful. Congrats and best wishes.