You have used a brilliant quote for the question, we know that Harry is, in terms of survival, Voldemorts most significant kill.
Up until he is cast from his body he has used objects with significant historical value, either to himself or to everyone.
- His own diary
- Slytherin's/Gaunt family ring (resurrection stone)
- Slytherin's Locket
- Hufflepuff's Cup
- Ravenclaw's Diadem
The pattern would Strongly suggest that the next Horcrux was likely to be owned by Gryffindor, however the only known surviving artifact or Gryffindor's is the Sword (which was presumably in Dumbledore's office)
I would like to state that we do not know what the Horcrux process requires we know that you need to kill in order to split your soul (it is also possible you need an additional process to split your soul), I've always been under the impression that the killing can be done in advance which will leave your soul in an unstable / split way then late you can begin the Horcrux process. I believe this because it is unlikely that he would take his significant items with him when he murdered and then perform the entire Horcrux spell at the scene. However, this could help to explain why upon revival he chose to use Nagini as his final Horcrux. If he lost his significant item at the Potter house the night he died he would need to find a new item for his Horcrux creation. I'm fairly certain that Dumbledore would have scoured the Potter house and found anything of any significance.
As a side Harry may only have been the precursor to his most significant kill of all, Dumbledore. With Harry gone it is likely that Voldemort would have no fears, he has squashed the prophecy that was to be his undoing and now he will take on the only other threat he has. Killing Dumbledore and then using the Sword of Gryffindor as a Horcrux. I feel this can be related to my earlier point,
As talked about here Voldemort did not have Nagini until after he died, so she is ruled out.
Like previously mentioned an object of significant sentimental value, something from his childhood or time at school is most likely. This could even be something belonging to his favourite teacher Horace Slughorn.
Something else he found of great historical value when he was working at Borgin and Burkes. Borgin and Burke were in the business of acquiring great dark artifacts, it is possible that Voldemort had one that had some significant value to him.
Personally the most likely Horcrux of choice was the Sword of Gryffindor I think after ending the prophecy it is likely that he would have gone onto try to kill Dumbledore (he would after all believe himself unbeatable), or by the very least steal the sword for his final Horcrux. Upon returning to a more normal life and after being "killed" his fear of death would have grown, forcing him to create his final Horcrux and as he would have believe the seventh fragment of his soul (Seven being the most magical of all numbers) he would have believed this to make him more powerful as well.
We may never know the precise answer, until JKR really goes into depth with the Horcrux stuff.