I was not expecting this much traffic right off the bat.

The carpet is worn in the middle where foot traffic is. 

But, if you can afford it, I'd put a little fridge in each unit and a microwave, and maybe even a little coffee maker, to lessen the traffic in the kitchen.  

You know, since that guy is acting like he has the right to go do what he wants on your property, what you might do instead of putting up signs, is send a letter to the adjoining property owners, just saying you've bought the property and want to stop the foot traffic through it, and here's your contact information, and please let them know if anyone goes onto the property, as someone's been vandalizing your plants.  

I am trying to group people so that I can minimize the traffic but not sure how that can work without me losing a potential good tenant trying to schedule it for when they can be there for me to show.

It highlights , suspicious activity, High Traffic, as a Zero Tolerance lease violation.If it were me I'd give them a mutual lease termination notice,, give them a week to move, return the deposit, if apartment is left broom clean and they are out.

Auto accidents on premises are not a landlord liability matter, generally, I say generally because you can be found negligent if you fail to provide reasonable traffic notices, signs or warnings for drivers.

Unless this unit is hard to rent, you have had minimal traffic, etc.

If they say yes, I schedule a showing.If they are late and don't call me with a good reason - they're stuck in bumper to bumper traffic - denied.If they don't fill out the application completely, after I hand it to them and tell them I need it filled out completely - denied.If they say they're going to drop something off by a certain time and they don't - denied.You can actually screen them out pretty quickly, and without having to show the unit to that many applicants.But, just remember that you will get probably 10 loser applicants to 1 decent applicant - and just because they are trolling all the ads, playing a numbers game, looking for that one naive landlord who will rent to them.  

They'd have to normally go to work, possibly have to work late, get stuck in traffic, pick up kids, etc., and remember to get a check to you wherever that would have to happen.Just don't set them up to fail, is my advice.