Ways of Screening/ Filtering Potential Clients?

First thing I would say is listen to your instinct! One client that rubs you the wrong way will eat more time and energy than 10 like minded souls.
Now I can also say that some clients have taken me to task initially to make sure I had a clue then softened up after a few answers. For example I have responded with nobody can guarantee you 1st spot on Google to have them reply thank god you said that I know that's a scam.

As you get better at what you do and have satisfied clients that recommend your services this will get much easier.

I have some offers for example that simply require too large an investment and too close a working relationship and as such I only take on clients that have been referred by an existing client. My existing clients for this service are very close to me and only recommend people they already know would be a good fit.

Before you get to that point simply change the conversation.
Don't engage in conversations on why he should pick you.
When someone says I want you to guarantee me spot 1 and they are serious ask why?

I say to them I am in the business of helping my clients profit from the web.
If you believe that someone can guarantee you a top spot and if you believe
that simply having a top spot will make you money, I would suggest doing more homework before choosing a provider as you may fall prey to scammers and even if you don't you may quickly learn that the number one spot that cost you so dearly, for that phrase you thought was so important, is not delivering the results you thought it would.

I would then say I would be happy to discuss how I help my clients find hidden gems of buyer keywords, how I help them convert those rankings and visits to buying customers and how I act as their expert adviser so they can rest easy knowing the web is taken care of for them.

While I would never advise anyone to take a PITA client or customer I think you need to read what you just posted. It makes you sound like the PITA honestly.

1. You don't direct people when to call you. If it is a bad time you let it go to voicemail or pick up and ask them when would be best to call them back. This is customer service 101. The customer may not always be right. But they deserve respect. He wasn't disrespecting you so why disrespect him?

2. You told a guy you would call him back yet don't think you will? Ok wow I don't even know what to say to this. If you don't want him as a client that is fine but you need to do what you say you will do. If you say you will call back at 3pm you sure as hell call back at 3pm unless something prevents you and in that case you call back and explain and say you are sorry. Once again this is customer service basics.

3. You have competition so you better be convincing ever single prospect why they should be choosing you. This one just was being up front about it. if he isn't convinced you are the best choice for his business that is your problem not his. He has every right to get you to convince him. But he shouldn't have to do that. You should be doing that already. What is in it for them? That is selling 101.

4. We all work with people who need our services. The difference between a clerk and a salesman is the clerk just rings up the people who ask to buy while the salesman knows how to show someone why they should buy. "Tire kickers" do exist but if a business owner/manager is taking his time to talk to you they are likely not one. These people have busy lives. They don't have time to waste tire kicking. This isn't retail sales where you get a load of strokers. If these guys are taking the time to talk to you they are serious. They are buyers. Will they buy from you? That is up to you.

5. Your price is your price. If you are showing the value to them your price matters little minus people who like to "win". If it is a big job or a repeat customer consider discounting if it makes sense. Otherwise be ready to walk away. People are not used to salesman who are willing to be the ones to walk away. And pulling it away from them often works as a close. "I understand you have a budget Mr Customer. I would be lying if I didn't say I was disappointed that this will not work for you. blah blah" He who is willing to walk away is in control. If they are serious they will stop you before you leave.

6. Won't sign a contract? Why not? Hell if anything a contract protects them more than you if you are getting payment up front and you are getting paid up front (at least half) right? IMO a contract benefits you zero. They don't pay? You sue for payment and likely still never see it. You don't fulfill the contract? They sue and get a refund plus get to keep anything you did for them. Hell they can even get damages. So why wouldn't they sign a contract? It is for their protection not yours.

7. Client has unrealistic expectations? It is your job to give them realistic expectations. They want number one in NYC? Unless they are the only one selling something that competition will be huge. They can get there of course and you can help them, right? But they need to understand the kind of budget that will require and the time frame it will require. Educate them.

Another guy claims he can do it for less? "Sounds great Mr. Customer. I'm going to put a note in my calendar to call you back in a year, if you don't mind. I'd like to see if he can do it and plan to offer him a job on my team if he can. Our company is always looking for experts like that. We hire the best and it sounds like you believe he is the best. We have a great referral bonus you would be eligible if we end up hiring him. Sounds like an easy way to make $2,000 doesn't it?"

Even if you don't have a referral bonus for finding employees saying something like that will show him you only hire the best and are willing to pay to get the best. Plus do you honestly think this guy will pull it off plus take your job offer? of course not. You will never have to pay the $2k. And even if you did wouldn't it worth it to get that guy working for you?