Our goal is for me to buyout my siblings and to own the house myself while maintaining as much of the prop 13 tax basis as possible. 

Is it possible to have equalizing different assets going to your siblings? 

Is it possible?

I've called a few lenders and landed on one that's gotten me pre-approved for a loan so I know what price range I should look in.

When I started out, I did one flip at a time and here in CA, my acquisition prices (back in 2009) ranged from the $250k-$400k range.

I’ve looked at a couple new communities and do see the same price range as you.

While no one has a crystal ball, consider whether that amount is right for a downpayment for your family given the new area, home price ranges (which may continue to appreciate, especially if rates come down in 2024), and the resulting expected monthly payments on a new mortgage. $50k might be the right amount, but if you haven't already projected monthly P&I on the new home at $50k down, I'd recommend doing so before committing remainder to investments.3. 

Looking into getting into a beach condo possibly in the Florida panhandle. 

Yes, absolutely, but go into it knowing that it's possible, but also possible that you don't make anything or even lose money (similar to how one should look at buying stocks).

Looking at the properties on their website I see that they are all in the high $30K to low $40K price range.