This increased the required household income to purchase the median-priced home by $6,400, to $119,700, after also accounting for the cost of tax and insurance.

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

That question will require an essay to answer every part of your question :) With stocks, you mostly gamble on appreciation.

My thought process is to purchase the property initially under my name so that we can pay 5% down as my understanding is that mortgages to LLCs are more difficult to find, have higher interest rates, and require a higher down payment (around 25%).

But sometimes free can cost you a bundle if you violate local laws, or don't include something that is required in your state.

That said, I wonder if these are the kind of cameras that require "altering the property" in any way, because there is typically a provision in lease agreements that prohibits the tenant from altering the property without landlord permission. 

Of course, with all things, the answers to all these matters will depend on the circumstances.California tends to have more laws on the books and requirements and restrictions that it can be a good idea to form a CA LLC for out of state property so that you as a CA resident are covered, and to try to have your contracts fall under the purview of CA courts.

3. requiring heavy amount of rehab (siding, foundation, roof, HVAC, appliances)?

Not really, as long as you are up front with a lender, most would just require you to show them the establishment of the LLC/accounts and then could proceed with that.

However, that requires us to dig down the basement floor to meet the ceiling height requirement (it's got the egresses and 2 exits already), and I think that can easily cost us $100-120k.