Question 1: If you could go through a bin of random ancient coins, what would be an acceptable price per item? Question 2: What are a few things to look for to easily authenticate the coin and ensure it's not a modern knock off? Question 3: Of all the "stuff" these cheap ancients in a random bin are covered in, is there is anything I should look for to skip? Skip because it won't come off? Skip because I can't even tell what the coin is because there's so much gunk on it?
New Question 1: If you could go through a bin of random ancient coins, what would be an acceptable price per item? That's a hard question to answer; you have to be familiar with ancients to know what's a good deal and what isn't. If the coins are attributed and have good eye-appeal, $10-15; unattributed, $5-10. You have to be careful with such lots, though. Many are unidentifiable culls of no value. Question 2: What are a few things to look for to easily authenticate the coin and ensure it's not a modern knock off? Buy from a reputable dealer who guarantees authenticity. Question 3: Of all the "stuff" these cheap ancients in a random bin are covered in, is there is anything I should look for to skip? Skip because it won't come off? Skip because I can't even tell what the coin is because there's so much gunk on it? Avoid powdery, toothpaste-green on any coin. That's bronze disease and it will eat the coin away over time and pose a risk to your other coins. I'd avoid coins that are so encrusted you can't tell what they are.
I pulled all but the bottom row out of a $5 each bin. I left stuff that did not gave good detail, had obvious damage, or was completely encrusted.
Buying from an experienced and reputable seller is the easiest thing you can do to authenticate your purchases. As far as actually learning to authenticate coins for yourself it takes years of study and handling authentic coins and even then you might still make a mistake and have to be able to realize when you're out of your element. I feel pretty confident in my skills at authenticating most Roman Republic types after spending probably hundreds of hours studying them over the past 4 years but I still encounter the occasional coin that I'm unsure about and I can rarely spot even obvious Byzantine fakes because I haven't studied the coinage.