Welcome to the hobby,
I know for my first few batches, I didn't know anybetter so I just made an ice bath to cool my wort down. So cheers to you for doing you homework and understanding the importantance of cooling down wort quickly, it really does make a big difference in the finished product.
First, I would say that you will should be able to find fittings that will allow you to adapt your hose to whatever size copper you choose.
Second, I would recommend that you go with an immersion cooler. I have never owned a counterflow but I choose an immersion for the following advantages that I think it has over a counter flow.
1. Since the wort is exposed to the outside of the tube and not the inside, it is easier to clean and sanitize.
2. It is easier to monitor temperature control since you can just continue to run water through while you monitor the temp and then just it off when you hit you pitching temp. ( I actually like to chill down to 5 degrees below my pitching temp because I have found that the wort heats up a bit as it gets racked into the fermentors)
Personally, I would recommend 50 feet of 3/8" cooper. A thicker diameter will not materally increase the surface area exposed (meaning it won't cool things down any faster) but will increase the cost. A thinner diameter doesn't really supply enough water to maximize the heat exchange before the water inside the tube becomes the same temp as the wort outside. Also, just because the copper is expensive, don't cheap out on the length. If you move to bigger batch sizes in the future then 25 feet of cooper just won't cool it. Remember, you can't cool the wort down too fast but you can not cool it down fast enough.
You may also want to look at morebeer.com and look into just purchasing one. I found that once I figured out the material cost that it wasn't much more to just to buy one and that way I didn't have to worry about getting the fittings just right so that I didn't have any leaks...don't worry, you will have plenty of other DIY project with this hobby....
Anyway, that is just my two cents...good luck and happy brewing!