I was wondering if players were given debuts more away than at home, so I took look at the stats, and it's almost even!
The same number of players first appeared at the City Ground as they did on the road, and I'm actually surprised by that; I assumed there would be a higher count away from home.
And don't forget about those who made their debut on a Neutral ground...that's 10 of them! (For the record, they were all in the FA Cup in the late 1890s, or the 1959 Charity Shield.)

Home or Away Num Games Num Players

Debuts On Neutral Grounds
For the record, here are the 10 players who made their debuts on a neutral ground, and as you can see, it's pretty dismal. We haven't won a game! I guess that's why the last debut was in 1959.
Date Type Opponent Player Ground H/A Score
Sat Mar 22, 1879FA CupOld EtoniansJ BishopKennington OvalN1-2
Sat Mar 27, 1880FA CupOxford UniversityHenry BillyealdKennington OvalN0-1
Sat Mar 27, 1880FA CupOxford UniversityLeonard LindleyKennington OvalN0-1
Thu Feb 28, 1889FA CupChathamJoseph SouthallKennington OvalN2-3
Thu Feb 28, 1889FA CupChathamWA SimkinsKennington OvalN2-3
Sat Mar 05, 1892FA CupWest Bromwich AlbionThomas HamiltonMolineuxN1-1
Sat Mar 24, 1900FA CupBuryFred ColesVictoria GroundN1-1
Wed Jan 16, 1946FA CupWatfordColin RawsonWhite Hart LaneN0-1
Sat Aug 15, 1959Charity ShieldWolverhampton WanderersJim IleyMolineuxN1-3
Sat Aug 15, 1959Charity ShieldWolverhampton WanderersPeter KnightMolineuxN1-3