First time Air Rifle Owner

Question
Hello Paul.  
I recently bought a Crosman Phantom Air Rifle as a present for myself, for target shooting and small game hunting.  When I was younger, I used to go out around the property (15 acres) with my Daisy multipump BB gun and get Rabbits and Squirrels (to the amazement of my father).  It was fun, but now that I am older I wanted something with a little more power.  I reviewed lots of guns and settled on a .177 Air Rifle over a .22 because I do live around neighbors and didn't want the distance that a .22 shell can travel.  
Well, the sites on my gun are crappy (as reviews stated), and cluster shots of around 20 give about a grapefruit sized spread.  I am not good at siting in the sites, so I bought a NCStar Tatical 4x20 Compact Air Scope to help with my siting.  As the reviews also say, my airgun is hard on the scope.  The rear eye piece was shaken off yesterday and I had only shot it maybe 15 times.  
So, My questions are, what is the best way to site in my rifle, and do you recommend any airgun scopes that will work better than what I have, ie Red Dot, Lazer, etc.  Also, I have a budget, but do want to get something that will make my shots accurate.
What is the best distance to stand away from the target to give the most accurate site reading?
How accurate are the manufactured sites on the Air Rifle I own?  When I turn the dial on the up and down adjustment, it doesn't look like it does anything, same for the L and R adjustment.  Its also cheap plastic rather than metal.  

Thanks for taking the time to read my question,
Kim

Answer
Hello, Kim.
  My name is Charles. I noticed you have been talking with Phil. I am not trying to replace him, or his expertise. However, I found your question in the Question Pool. I will try to answer your questions. I know you paid well over $100 for your Crosman Phantom. Break-open air rifles are what they are when you take them from the box. There are very few adjustments you can make to them. I would suggest checking on the Benjamin Titan GP Nitro Piston .177 or .22cal. I prefer the .22cal. for small game. It is priced about the same. It has a vibration buffer and very light break (30-33lbs.). There are no sights, but it has a perfect set-up for a scope. Not too much recoil. Check out the Benjamin Warrantee. Check with www.pyramydair.com for comparisons on many more brands. I hope this helps. Charles Gage