First of all, let me just say that I am so excited that you started a thread on beagles. Although I have done a lot of reading and research on the breed, I did not consider myself knowledgeable enough to start an informational thread on the topic. I will address some things already mentioned and some general information that I think you should know, but it would be really helpful if you asked some more specific questions. Keep in mind that anything I say comes from my experience (with only ONE beagle, all dogs are different) and the reading I have done. This may seem kind of sporadic, but I'm just going to spout off some random things about the breed.
No matter how well trained your beagle is, you can never trust him off leash. The hunting instinct is too strong, and it is true that they pretty much go deaf when tracking a scent. Oftentimes the only thing that can bring them out of it is the sound of a gun shot. Many beagles get themselves run over or lost from following their noses into streets or miles away from home. You do not want to take a chance thinking you can trust your beagle just to find out you can't. I made that mistake once. I've learned that Sampson is very reliable on his recall unless he sees a bird. If he catches sight of one, I cease to exist.
A fenced yard is an absolute necessity, and you must check it regularly for signs that your pup is trying to dig out. Sampson is not a big digger, but a lot of beagles are. He only digs where the ground is bare and no grass grows. I recommend a designated spot that is okay for your dogs to dig (kind of like a sandbox) so that your dogs can still perform that instinctive behavior. I do not have one because I rent my house, but I regularly take Sampson to the beach and let him dig to his heart's content.
Beagles are exceptionally good with other dogs, and they thrive when in a home with another dog. That is a big part of why I am considering adding another dog to my family soon. Beagles were bred to hunt in packs, so the pack mentality is very strong with them. Humans can definitely fulfill the beagle's need for a pack as long as there is at least one family member around most of the time. If everyone is gone for a good portion of the day (at school or at work for example), a second dog is highly recommended to prevent things like separation anxiety (beagles are prone to this). I do not recommend birds as pets when you have a beagle. Although beagles were bred to hunt rabbits mostly, mine has quite the obsession with birds. Although I think a caged bird would be okay, if the bird were released, it would probably be difficult for a beagle not to "hunt" it. Sampson has a tendency to want to chase cats when he seems them outside. My sister recently moved in with us and she has a fairly young cat. Sampson is actually scared of it. They aren't around each other much, but he has never tried to chase it. I'm sure that if you raise your beagle with cats there would not be a problem. Although your puppy might want to chase it at first if it runs. You must always expect that hunting instinct to kick in. Anticipating it and preventing situations from occurring that could trigger it will help keep your beagle and your other pets safe until they learn how to behave with each other.
It was said that beagles have a tendency to roll in poo. Thankfully, Sampson has never rolled in anything smelly, and that is not due to lack of opportunity. So your beagle may not have the tendency to roll in poo either. But, Sampson does like to eat poo. We are making some good progress in this area though. A good diet is really important. My vet said that dogs can sense if there is more nutrition available in the poo. If there bodies are not digesting the food well enough, they may consider poo just as valuable as food because it still has nutrients that they need in it. I seem to be having luck with adding more fresh meat (for protein) to Sampson's diet. It has made a huge difference.
I agree that training needs to start immediately. Please use positive reinforcement training with your beagle. They can be very stubborn and need to be motivated to do what is asked of them. You need to be very patient and I strongly recommend starting with treat rewards. Beagles are incredibly food motivated. Sampson will do anything for a little taste of a treat. I buy training treats that are easy to break and I break each one into 4 or 5 pieces, so we only use 3 or 4 treats per session. This is important because beagles are prone to obesity. Most beagles you see will be grossly overweight. Never free feed a beagle because they will eat too much. Always feed a high quality food and do not give them any fatty human food. Be careful to make sure you do not accidentally encourage begging. It is hard to resist those sweet little puppy eyes and floppy ears, but beagles are terrible beggars. If they get started, it is really difficult to break the habit. It is best if you feed the puppy after you eat. This will teach your dog two things: you are pack leader (leaders usually eat first) and begging will get them nowhere. If you consistently feed them at the same time, they will learn that regardless of whether or not they beg, they won't get their food any sooner or any of yours at all. If you do want to give your dog some human food, wait until you are finished and put it in his food bowl. If Sampson is good and does not beg during meals, I will give him something healthy off my plate in his dinner. This has been very effective in keeping him from begging while we are eating. Beagles can be pretty challenging to train. They have are stubborn and have an attitude. They are notorious for being difficult to potty train. Sampson has been pretty easy, so I got lucky. He was potty trained in like a week and a half. He knew his routine, and he knew how to ask to go out. There were only a few accidents after that and they were due to overexcitement and inability to control his bladder because he was so young. They aren't able to really hold it for any length of time until they are several months old. But the basics can be taught in a short amount of time, and as long as you are consistent and anticipate his needs there won't be any accidents.
Beagles are prone to ear infections because of their floppy ears. It is very important that the ears are cleaned at least once a week, and this practice needs to start immediately. Sampson got an ear infection two weeks after we got him because I didn't realize how important it was to start a regular cleaning routine immediately. Ear infections are extrememly painful and can cause deafness, so I can't stress the importance of this enough. I now have a routine where I clean Sampson's ears twice per week with ear cleaning pads bought from a local pet supply store. He has not had another ear infection.
Another important thing for beagles is to make sure they get adequate exercise. Sampson gets three walks a day. In the morning before I go to work, on my lunch break, and after work. He also jogs a couple miles several times a week with my husband. Although jogging/running releases his energy faster, walks are important for beagles because they exercise their mind. The smells that they get to experience and track if you let them really stimulate the brain. Beagles were bred for their ability to smell, so it's important to let them exercise that. They will quickly get bored with the smells in their yard, so be sure to take them elsewhere to sniff around and explore (on leash if an unfenced area).
Well I hope that helps somewhat. Feel free to ask questions. You can never be too prepared.