I was going to put the exact same info that Kazbah put from beagle rescue vic. My DH and I nearly fostered a beagle pup for them (it fell through when a more desperate little puppy came into our care) and they gave us a mountain of information and even came out to the house to make sure our yard was "beagle proof". Their recommendation was to half bury wide planks of wood along the fence so that if the beagle tried to dig under the fence they would also have to dig the extra distance under the planks of wood you buried.

One of the most important things to remember is to NEVER EVER let a beagle off leash in an area that is not completely fenced off. The just catch a scent and run with it and nothing will stop them. Give your local councils a call and ask if there are any completely fenced off dog parks in your area. They are great for beagles

If you are planning on pup travelling in the car a bit, then best to get it used to the car ealy. Lots of pups get car sick to begin with and then grow out of it. If you pup seems to get anxious about getting into the car, start slowly by taking it out to a the car (with the car turned off) and give it some food in the car. Do that for a few days. Then do the same for another few days, but with the car running but stationary. Then you can move up and down the driveway, then around the block etc etc ...

Most of all, just enjoy the new addition to your family!