We have a puppy pen for Bella but only use it at night for her to sleep in (in our bedroom but it means she goes clean through the night and also doesn't try to chase the cats who also sleep in there!).
Tried a baby gate but Bella didn't like it at all - she is fine to be left in the kitchen on her own with the door shut but cries like crazy if she's in there with the baby gate on - it seems to make it worse for her if she can see us walking around but can't get to us but if she can't see us she just settles down and goes to sleep.
The puppy pen at night has worked well for her - she has been clean through the night (8 hours) for a few weeks now, so much so that we are gradually increasing the space she has and hoping to actually let her just sleep under the bed with no pen very soon (she is quite good with the cats now as well so not worried about that anymore!).
Like others have said - whatever works for you. Bella is usually in the same room as us although does take herself out to the carpet in the hall to play with her toys on her own. Her bed gets moved in the daytime into the kitchen and she quickly got into the routine of this - it doesn't seem to bother her at all!
Good luck with your pup!
Claire