Here the county shelters charge $75 for adoptions, and while that includes spaying/neutering and basic vaccinations, it doesn't include a heartworm or fecal test, heartworm preventative, or flea/tick preventative. The rescue groups charge around $150 (the purebred rescue groups charge $250-300). But this includes everything. So I find rescue groups to be a great "bargain"!
Besides, good groups work on housetraining and basic obedience and can tell you more about a pet's behavior in the home than a shelter can. And if you adopt from a rescue group that rescues from shelters, your new pet will leave a vacancy so another shelter animal can be rescued by the group.
But adopting straight from a shelter is a wonderful thing to do. You really do save a life. Compared to the dogs in shelters, rescue group's dogs are the lucky ones. You know less about the dog going in, but if you're patient and committed to working through any behavior issues, that shouldn't be a problem. There are knowledgable pet people here--even trainers who can help you if any problems crop up.
Beagle mixes are great! Beagles can be great family dogs. Just be aware that they like to go on adventures, so make sure your yard is secure. We fostered a sweet beagle who kept digging under the fence to get out--even though we never left her outside for more than 20-30 minutes at a time. My husband had to "plant" bricks underground just inside the gate of the fence so she couldn't dig out. We couldn't ever let her off leash in the front yard.
We just adopted a shih tzu mix two weeks ago. He's a great little dog who loves kids. We adopted him from the rescue group I used to foster with. He was on his best behavior the first week and then the chewing up stuff started! But he's still MUCH easier than a puppy would be!
Congratulations on your new family member!