It's highly doubtful a definitive direct ancestor to both urodelans and anurans will ever be identified, but Lissamphibia are usually suspected to being derived from within Amphibamidae [Temnospondyli]. Alternate hypotheses suggest Lyssorophia [Lepospondyli], especially for either caecilians or caecilians and salamanders; or Microsauria. Within Amphibamidae, the main suspects are
Amphibamus and
Doleserpeton.
Would like to see what that would look like. I'm guesing an awful lot like a salamander.
That's a truism. Frogs had a highly modified [derived] body plan, whereas salamanders have a very universal plan, that of a tetrapod with four legs and a tail [ie, a plan shared with modern reptiles, turtles, fossil "amphibians", crocodilians, dinosaurs, some fossil snakes, one fossil caecilian, limbed transitional fishes, and most mammals]. Temnospondyls and most of their derivative groups, like Lepospondylia, Microsauria, Lissamphibia, and Amphibamidae, almost universally share this design.
On this question though, proteids are not relevant. They're not close to the origin of either salamanders or modern amphibians, but are a fairly recent derivation within modern salamanders. Older hypotheses suggested different origins for North American and European lineages, but the best recent data suggest the two to be closest kin. While sharing recent origin, that origin is still old enough for a land/freshwater link between the two lineages. The modern continents are really very young, relatively speaking. It's interesting that although the two lineages have similar numbers of species, the Old World [Proteinae -
Proteus] is almost exclusively subterranean, while the New World [Phanerobranchinae -
Necturus] is exclusively epigean. I suspect the karst habitat had little competition in Europe, while epigean habitats either retreated into the karst, were lost entirely, or suffered competition with various newt lineages [many of which are now extinct]. In North America, stream habitats of all kinds were either occupied or quickly colonized by plethodontids, the latter seemingly being the first to take over the mountain stream and subterranean habitats. Thus,
Necturus remained restricted to the same habitats it now occupies, and
Proteus habitats gradually retreated into the limestone.