Anyway, with these goals diverging in some ways, I'm feeling the pressure to ensure that I present him a great deal and pick a winner first thing.

Pick a solid B-Class suburban area.

This property is in a great area for me in North Arlington (great schools, stones throw away from a huge community park, and close to I30), and the plan is to live in it for a year or so before renting it out (I’m sure I’ll be picking your brains when the time comes!). 

Ocean lakes in Myrtle is probably your best bet. 350k may get you a 3/2 which will gross around 45k per year. 2-3 years ago you could pick up a 4/4 or 5/3 for that price so you may be priced out but there are a ton of condos for that price of 350k although I wouldn't buy a condo there we have two 4/4's but we stole them before pricing went crazy here in ocean lakes.if your diligent you can still find a deal but is much harder now 

Sounds like you picked a bad tenant, so start eviction ASAP.

Get to know that market well, the  class of neighborhoods, and don't pick a random Midwest city just based on numbers someone is telling you (e.g it will cash flow x amount $$$). 

Cash offer do carry weight as they can close quicker, don't need appraisals etc, but as an agent that works with buyer and sellers, I've seen it many times where a seller will pick a different offer due to some connection to the buyer (ex military, young married couple just starting etc) They want to know its NOT going to an investor specifically. 

A great rule of thumb is to underwrite 100 deals before picking one so that you can develop another sense and start to smell out the great opportunities when you find them.

In the meantime, I plan to cold call opportunities I picked out that look promising.

You could pick any spot on the map and probably make a good investment.