The biggest thing is to just get comfortable, then build your confidence. Get your footing, every time you step up to your put get your footing set. that is where all your power comes from is a stable base. Start short when you practice, don't start at your problem areas, in order to build your confidence you need to start short hit all those 5-10 footers, then move back to 10-15 footers. Make sure you remember how the good putts feel coming out of your hand. One thing that has really helped me with my putting is a line from a movie, The Patriot. Mel Gibson tells his sons to aim small, so that if you miss you miss small. There is a video that Eric McCabe did on putting, the McCabe minute, and he says he aims for one chain link, same concept.
As far as what putter you should use, that is entirely up to you. The questions you have to ask yourself are, what do I want to disc to do, do I want the disc to be straight, or finish into the basket? Do I want the float and glide, or do I want it to drop fast? The last of these questions should always be how does the disc feel? If the disc doesn't feel right in your hand you are going to doubt what you are about to do.