In my case, if each of my two properties will be set up on their own LLCs and bank accounts, where do the funds come from for the subscription fee on the tenant management software that manages both properties?

I currently use Buildium, I find it's a good software for a Property Manager but not for an owner operator.

Do you utilize an accounting software already? 

There’s lots and lots of softwares that help you find who the owner is.If the owner is motivated and wants to sell, then you use a Purchase and sales agreement to get the property under contract. 

Do you have any specific software that you would recommend to any project managers just starting out or trying to transition to new technology?

Get one that can be tied into your Operations software, and not maintained on a side system.

Cost to find the deal was marketing and CRM software.

@Phil C. as an Appfolio user since 2009, you would think that if you have AppFolio software that the transfer would be seemless?

I was searching some real estate analysis softwares and found there are couple of web based software  that also have database and comparable for all US properties.

I accept online payments via Tenantcloud- that's a PM software that offers a lot of features for landlords and PMs.