I would recommend a bitch, purely due to the fact that you have 4 and 5 year olds my reasons:
Bitches mature faster, and you don't get all the testosterone problems, GR's are lovely friendly dogs of good temperament, (as long as from a reputable breeder) but young male dogs especially the size of a GR will almost certainly attract other males trying to put him in his place, GR's are bouncy and known for being diggers, with having young children I think the smaller the better a large big boned male GR pounding towards you might not be a nice experience until properly trained.

With a male you may have a lot of unwanted attention and behaviour issues that with a young family you are best avoiding.
Dogs are more likely to follow you around and are known for being more loving in most breeds, but to be honest female GR's are just as friendly from the ones I've experienced, they are just more grown up! Which with a young family I think is something to think about.
Yes, bitches have seasons, but after the first you can spay, and yes, the amount will be much dearer than having a dog done.
As you've gathered I'm advising a bitch for you.