Brittanicus wasn't born until 41, and I think Claudius married Agrpinna around 48/49, adopting Nero shortly afterwards.
Brittanicus would have a very strong claim until 48, when his mother was caught up in a massive sex/treason scandal. I don't see Nero's death affecting the outcome of the scandal, but his death would make his mother a poor choice for Claudius' next wife for a few reasons. Claudius was Agrippina's uncle, and while a certain level of incest was tolerable, this was crossing a line. The scandal was worth it, however, as Nero was the grandson of Claudius' much-beloved brother Germanicus, which makes him a very attractive heir. Without Nero, I do not think Claudius would marry Agrippina. Who he would pick as his next wife is an interesting question though.
His freedmen advisors suggested a few of his previous wives, such as his second wife Paetina. This was suggested by probably Claudius' greatest advisor, Narcissus. It is overall a good match, and they already had a child together, and Paetina was a very caring and matronly figure which led Narcissus to think she would learn to care for her adoptive son Brittanicus. The only snag in this plan is Paetina was an adopted brother of Sejanus, which is why the divorce occurred in the first place, as Claudius did not want to get caught up in those purges. Sejanus was hated by the populace, but it had been almost 20 years since his downfall and death, during which the Roman people were treated with the apathy of Tiberius followed by Caligula being Caligula. It might have caused a small scandal, but I think it is probably the best match I can think of, but I am not very well-informed on Roman Noblewomen in the 1st Century AD.
With Agrippina out of the picture, Claudius will probably make it to 59 AD at least. By that time, Brittanicus would have finally become a man and donned his toga, which would likely have Claudius give him important postings or even a co-ruler status. Claudia Antonia's status might rise with the ascension of her mother to empress, and so it is possible that she tries to marry someone of higher status than Sulla. Given the concerns of merging the Julian and Claudian portions of the imperial family, which Claudius hoped to solve by using Nero (Grandson of Germanicus and Grand-nephew of Augustus himself), I think a well-placed marriage for Claudius Antonia could unite the two branches.
A very good candidate for such a marriage would be Silanus the Elder, a direct descendant of Augustus. Silanus seemed to have been a competent politician as well, a good trait to have in the Imperial Family. A marriage between Silanus and Claudius's other aughter actually almost happened in reality; Claudius betrothed the two, but Agrippina convinced him to nullify any such promises.
Silanus, and his children by Antonia, could have potentially been rival claimants to Brittanicus. Claudius' death being pushed back a few years lessens the odds, but it is very possible. The people generally preferred the Julians to the Claudians, so if he wanted to, Silanus could use good PR and decades of experience to potentially crush Brittanicus in a succession crisis.
EDIT: I just realized Marcus Antonius Primus was alive at this time, and he was a very gifted general who handed Rome to Vespasian on a silver platter. He could also trace his ancestry to Augustus and Marcus Antonious, and could have been a contender if he had gotten one of the Claudias as his wife. Good pedigree, tactically competent, and fairly ambitious.