Which is the best nail dremel to use and where can I buy it at the best price?

What is the best is really up to you. Do you want portability? Would you take it with you to outdoor show weekends for touch ups? How many dogs do you have to do? Do you have other breeds with really big, hard nails, like Ridgebacks, which really need the old fashioned plug in rotary tool if you have a lot of them? Or do you also have little dogs?
I personally like the type that charges in the wall, but is cordless, and does not have a household battery. That can be a Dremel mini mite (?) or, in my case, a Craftsman knock-off that fits the same things. I can sit on the floor rubbing my dog's belly then grind nails, or be outside on the grass or anywhere and not be tied to a wall socket. No cord for the tail to thump or a puppy to chew. The battery ones are not so scary if a tail loops up and hair gets caught in it--the thing will grind to a halt instead of ripping out the hair and skin on the dog like the big plug in Dremels.
I'd say do NOT get the metal nail grinder--those suckers get hot. Use a sanding drum, and move it around a lot. Don't just grind one nail at a time. For those who were scouts, remember that friction is used to start a fire with a revolving stick. For those who do the beauty thing, it is like using a nail grinder on nails at a manicurist for people--any of them get HOT!

The ones with the guards are harder for me to use.

You could ask friends to give you a demo or trial run with theirs!

I like the cordless I got from Sears. It's a craftsman and is still going strong after almost ten years.

The Dremel with the Lithium Ion Battery cordless is just wonderful. I would check the "Big Box" stores around Fathers Day

I use the Black and Decker rotary tool - it is very sturdy, ergonomic, and the cord is very long. I like it a lot better than the Dremel. Read the consumer reviews on the products made especially for pets... One safety warning - wear glasses or safety glasses when grinding nails!