This is a troublesome subject because, as has been previously stated, since they don't plan anything that happens in an episode it often ends up contradicting previously-established information, either from other episodes or, indeed, earlier in the episode itself.
Here's what little, conflicting information we have, which we probably can't use to ascertain the true parentage of Littlebutts, N.C.'s premiere expert in paranormal investigation (aside from the British chap)
Now he was the first mentioned, as we all know, and that was only in (as far as we know) the Cardboard Friend Mod 2. As Ghost said in the episode, Timothy, or "Tommy" as he's later called, died before Ghost was born. He also stated that at the time of his death Casket had amassed a quite a large sum of money - apparently large enough to keep him and his mother afloat and get him through school (I don't understand the American education system, what we have over here is primary school, secondary school and college, and then Uni if you're really, really talented and/or really, really rich.)
That Deathmatch in the desert during the Galaxy Exploder episode, Jonn and Toast's father John are seen fighting together against an unknown enemy. Of course, I'm not sure they count as canon since they were speculating at the time, rather than roleplaying.
Pee Wee Ghost
I guess since he's the most recent and has been mentioned in the most episodes (2 - the lollipop mod and the Godzilla McDonalds). However, Pee Wee was said to be the most prolific ghost hunter of the 50's - at least 2 decades (maybe 3?) before Ghost's (assumed) date of birth (although it's hard to keep track what with Ghost's age shifting around so much, and that's before we even get to the time travel...).
Apparently Johnny Ghost's first appearance in the Kermit the Frog video was NOT Johnny Ghost - according to Ghost himself - but his own father.
Unknown (but not Phasma, we think)
This was WAAAAAAAY before 7 came out when Johnny's mother was first mentioned. There's too many times to list on here but the abiding memory for me was her being very protective of Ghost, especially around Toast, whom she considered a dangerous influence due to them always conducting dangerous experiments together - which, ironically, Toast's mother tried to keep Ghost away from Toast for precisely the same reason (although both seemed to think that the other one's son was to blame). She gave Ghost Barbie's and was horrified when Toast gave him an Action Man to make up for accidentally messing them up. During the Tom and Jerry Hospital in the Dream Dimension he said his mother was dead, started crying, and then changed his mind and stopped. There was some other stuff I was going to bring up, but I can't remember what it was. I'll have to rewatch that episode, if I can find it.
On a separate note, one of Casket's secrets was "my mother was a man!"
Apparently, durOMG that one where Kylo and Ghost steal the TARDIS for Phasma's daughter, we discover that the daughter IS Ghost. Not only does that not make any sense, that doesn't even make sense.
Updated to include Hide The Pain Harold. Not even gonna talk about this one.