We will be taking up Gibbon's narrative with Constantine's activities as sole emperor. The wikipedia article on Constantine (usual caveats apply) directs us to this excellent numismatic site dedicated to Constantine, which usefully gathers many of the principal written ancient sources in one place. Books 8-10 of Eusebius' History of the Church are also of interest (incidentally, CCEL's new format makes online reading much more difficult -- although you can download .pdf files if you register with them). Another source is the anonymous work Origo Constantini Imperatoris, also called Valesianus after its discoverer. LacusCurtius has the Latin and an English translation.
Smith's Biographical Dictionary has an article on Constantine (as Constantinus I), while DIR has two.
Those with money or access to a good library might be interested in this sourcebook
, reviewed by BMCR .
Another work which might be worth consulting is the Cambridge Companion to the Age of Constantine
.
As well as the Gibbon, I'm reading Charles Matson Odahl's Constantine and the Christian Empire (which I see received a not very favourable review from BMCR). 
