Bummer getting nailed twice in 10 minutes. While I am also in SoCal, I don’t have a factual answer, but I suspect they would count againt you equally since they are both ‘moving violations’.
If it was me, I would go to traffic school for the more ‘proveable’ violation (which in my opinion is the speeding), because the cop will probably have a radar gun readout or will have matched speed with you if he nailed you from behind. I think this is harder to fight…unless there are unusual circumstances in your favor. I’m assuming there aren’t
If you are going to eat it on the other ticket (stop sign violation) and can’t otherwise go to traffic school, why not try to fight it? My recommendation is to go to the courthouse, and do a “trial by declaration” so you can write in your defense to the judge. The advantage to this is that 1) you don’t have to miss a day of work in court and 2) the cop has to send in a written explanation, which is a pain in the ass for them and they might not do it, forget, etc. in which case it gets dismissed in your favor. If you try to fight it in court, you may not like the confrontation of it, and the cop is virtually guarnateed to show up since they get overtime, like doing it, etc. People don’t like to write (cops included) so I think you’ll have a better shot.
The “trial by declaration” will require you to pay the fine up front, but if the judge agrees you are not guilty or the cop doesn’t write a response, you get your money back. Anecdotally, I used the “trial by declaration” trick to fight a speeding in a school zone violation last year and won. The issue was whether “children were present”, which they were not, and I was able to prove that with a form from the school that showed their hours.
I’m also guessing your stop sign violation was a classic “rolling stop”, which is subjective. I’d try to argue that you did stop, there were no other cars, the cop was too far away to clearly see, it was dark, etc. Be professional in the letter (address it “Your honor” and “the officer” or “Officer Johnson”) and cite as many of the relevant traffic codes as you can. If there is even the tiniest mistake on the ticket write up focus on that too. What’s the worst that could happen? I picked up the forms on my lunch hour and wrote up my explanation that night. Three months later, I got my money back.