Once you have a relationship established, you talk numbers.

Well, you can liquidate and invest in Real Estate syndications, start up businesses or established businesses, hard money (still semi-active), NNN lease properties or put your money into stocks, bonds, mutual funds and gold. 

This would have established, among other things, which appliances were owned by whom.

You need to start at the end (the exit strategy...desired profit and/or cash flow) and work your way backwards to find the market (micro-market) that provides you with those properties/deals.The first numbers you need to establish in your analysis are, depending on your exit strategy, either your desired profit or cash flow. 

Ive had conversations with my grandmother in attempts to explain to her the value of the property and potentiality to establish wealth thru renting, but shes tired and wants to get rid of it.

Lots of comps to establish a good ARV. 

One additional Pro - you can take all the cash flows coming into the LLC and set up a bi-monthly or monthly "salary" that you pay yourself/your spouse in order to establish the type of income (W2) needed to qualify for mortgages in your personal name.

I also like to establish a dialogue with the Sponsor well before doing a deal with them.

And then you will need to establish some kind of track record of receipt to establish stability of the new income. 

Also, you don't want to establish her dependency on you so early on.