Congrats on the start of your adventure
The Southern Tier was my first self-supported bike tour, and it got me totally hooked on bike touring. I also started from SD at the exact same time of year that you're going; the first two days had a lot of relentless climbing and really kicked my butt. Don't give up! Once you get over the Sierras, it's all smooth sailing! I don't know if you'll find any campgrounds in SD at the start of your trip. I stayed with friends and my riding partner stayed at a hostel near Dog Beach. I encourage you to sign up for Warmshowers, there are dozens of people in San Diego who will give you a place to stay for free and probably feed you too. The Warmshowers network is international and I have used it all across the US and have hosted people from all over the world at my house in Northern California. It's free, check it out: warmshowers.org
Your gear list is very spartan, perhaps you plan to bring more stuff but didn't add it to the list yet. If the list you're showing is accurate, here are a couple of comments:
1. Don't forget to bring a towel - I use a microfiber camping towel from REI because it dries quickly
2. I don't see any non-bike clothes or shoes on your list. To get to St Augustine, you will be on the road for nearly 50 days at a minimum. If all you've got are two jerseys, you will come to hate looking at them by the end of the second week. I packed two tee-shirts and a pair of convertible long trousers (zip-off legs) plus some shoes for off-bike wear.
3. You must have a warm jacket and leggings as it will be cold at night, and during the day when the wind is blowing.
4. Bring soap so you can wash your cycling clothes every day, they need a day to dry before you need to put them on again.
It's a great ride, I wish I was joining you but I'll be preparing for an entire summer cycling around Europe. Have fun!!
Dan