Depending on your budget and location that you want to be in, the newer areas have homes and larger garages that have a fence. But as far as protecting your dog, unless you're out there with them, your dog will be an easy target for predators. Keep the dog screened in the lanai/birdcage. But, I also have read that some larger animals can bust through your screen also. So, our fur babies should NEVER be left unattended.

2 car garage
 

We rented a CYV with the 1 + squeeze in a golf cart garage for 4 years. We've since purchased CYV homes and both had 2 car garages. Why anyone would want less than a 2 car garage doesn't make sense to me. Extra storage is always a plus. Also think about your resale value.

In Florida, a 2 car garage means 2 small cars at best.

Lifestyle visits are a great way to get a taste of The Villages. You'll enjoy it.
For me, a one-car garage is a non-starter. That situation might work for some, but I think nearly everyone would recommend something bigger.
There are cottage villas with straight-in driveways and larger garages in the newer areas.
I'd also recommend having a look at the veranda series homes. These homes have fenced-in back yards and you have many floorplans and garage options to choose from.
I agree with the replies that recommend a 2 1/2 car garage. You won't regret having the extra space and it will be an attractive resale feature in the future.

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Get a Bigger Garage
 

We have a two stall garage and can fit one SUV, a small car, and the golfcart if we put it in sideways. My advice, get the biggest garage you can get because storage is minimal. We are constantly moving the golf cart when we want to take the small car out. It's a pain...