Who is credited for establishing the first Christian church in Rome?

Answer 1

Peter is usually credited with establishing the Church in Rome. There is a wealth of evidence, both documental and archaeological, that Peter and Paul ended up in Rome. While it is probably true that there were Christians in Rome long before Peter and Paul's settlement there, most scholars believe that it was Peter who established the Church there as a dynamic group of Christians from a scattered Christian population in hiding.

Evidence for this includes the catacombs beneath the ancient city of Rome, where there exists a great deal of grafitti on the walls that refers both to Peter and to Paul, and to their presence in Rome. There is also a great deal of evidence that after the executions of Peter and Paul their bodies were taken and concealed in the St Sebastian Catacombs whch run under the Appian Way leading south out of Rome, only to be reinterred in their respective basilicas after Christianity became accepted as the religion of the Empire, St Peter's remains being interred in what is now the Vatican City, and St Paul's in his own Basilica on the southern side of the city.

So, whether or not the church in Rome was 'founded' by Peter or Paul, they were well known to the Christians there, and there is much evidence that they ended their days there by execution, but not before a large Christian Church was established by them.

Answer 2

Paul's epistles are evidence that there was already a Christian community in Rome in his own time, while Peter was still in Jerusalem as one of the pillars of the church there. Thus, neither Paul nor Peter was the founder of the church in Rome.
Christian tradition holds that Peter became the first bishop of Rome, although there is no evidence that Peter ever went to Rome. Clement of Rome seems to have believed that Paul went to "the west" (Spain) after visiting the Christians in Rome.