How much cash would be sufficient and how exactly is it more simple to complete the transaction with some cash upfront? 

When the DP is not sufficient to cover the damage chances of collecting the short fall is zero to none.

TurboTax has been more than sufficient for me.

If you meet those criteria, you will have sufficient financial margin to make a profit even if the market tanks (in fact, that is precisely how I reverse engineer what a great deal is).

I'd rather use that money after maybe 2-3 years to buy something else that provides even more income.One could of course just sell the place but that might not be of interest if it cash flows nicely and otherwise doesn't have any real issues.Others might bank on sufficient appreciation but that would, I guess, again mean a loan to make use of this appreciation: back to the higher interest rate aspect.So yeah, how do people go about this?

FHA requires 3-4 unit properties to be self-sufficient, which simply means the piti (principal, interest, taxes, & insurance) = 75% of the current rents and/or market rents (whichever is lower).

My primary goal is to build a portfolio that will provide my father with income in semi-retirement and a sense of sufficiency.

I did the exact same thing and dealt with similar suspicion from the lender, but a detailed letter explaining why I was moving to the new property(bigger, nicer area, etc.) was sufficient for the lender.  

When presenting an offer do you typically do so within a contract ready to be signed or could it just be on something less formal ('napkin') needing more or less a verbal agreement soon after which you provide seller with a contract to sufficiently look over, possibly with some  attorney/consultant then officially sign? 

If there is sufficient equity in the CA property just use it.