I must admit I cant think why anyone thought this cross was a good one except maybe to bring some longer snouts into pugs.
As a past and present beagle owner I can say they are hunting dogs first and foremost despite the cute looks and I agree with @parus
that the idea of a dog determined to hunt but without the breathing ability is an awful concept.
I know they look cute but health is the most important consideration here, does this cross benefit the dog?
Apart from this a cross is always an unknown factor. With a breed there is always information out there to help you in making a choice and knowing what to expect when you get a cross you dont know which parent the dog will take after will it have more of the pug traits or more of the beagle? The bank of knowledge available to you as an owner shrinks because of the cross and therefore any behaviour or health problems you encounter might be just that bit more difficult to figure out.
As the OP is an inexperienced dog owner I would rule out anything beagle... I love them dearly but they are NOT an easy dog and even half a beagle is job for an experienced owner..