Amphibians diverged from fish much earlier than mammals/marsupials diverged from other tetrapods.  The mitochondrial genomes of vertebrates evolve roughly 10-fold faster than chromosomes in the nucleus, so this deep in history the mitochondrial genomes can be beyond saturation with mutations.  This does not prevent mtDNA from being useful and accurate for answering many phylogenetic questions, but it is something to consider when selecting genes or gene regions to study.  For nuclear genes, an issue to consider is how many species have been sampled and sequenced for any particular gene. 

So, the "ideal" gene or gene region is often a trade-off between several factors such as how much good historical information is in the gene and how many species can be compared using a given gene or region of the genome. 

It is usually best to consider more than one gene, perhaps a combination of nuclear and mitochondrial genes, before drawing a conclusion, because horizontal gene transfer, mislabelling or misidentification of species in GenBank records, and other problems can affect at least some entries in most data sets. 

One problem you will have with your quest here, is identifying which sequences in your data have been classified as "frogs" and which have been classified as "toads", because this will not be found in the taxonomy of the organism name in the database records.  It may be difficult to build a tree and then say "color the branches which have dry-skinned organisms brown and color branches that have wet-skinned organisms green", you will fist have to add a code to each sequence name indicating whether it has been called a "toad" or "frog".

A cool site to explore before diving into your work is the ONEZOOM tree of life at onezoom.org.  At first it looks a little "cartoonish" but if you take the tutorial you will find how to really dig in and switch between "common names" and Latin names for each organism, for example.

http://www.ncbi.nlm.nih.gov/pubmed/23666244

http://www.ncbi.nlm.nih.gov/pubmed/26454873

With the way technology and costs are moving, if you want to be doing this type of work, I would highly suggest doing whole genome sequencing to make these deep comparisons.  The costs for this have dropped enough to make it feasible and the large dataset will help resolve where answers may fail using few genes.

I can't answer your question directly because I know little about how molecular people approach this kind of question, but I would not put much confidence in the ability of any tree constructed on a single gene to accurately reflect evolutionary history (assuming that you believe trees do reflect evolutionary history). There are some thorny philosophical issues here that should not be avoided, although they frequently are. As a general principle it is best to avoid a priori judgements about what kinds of evidence will best reflect evolutionary history. Given your task you cannot avoid making such a judgement but it's a good thing to keep in mind. Molecular phylogenetics traditionally has relied heavily on mitochondrial genes or gene regions to reconstruct deep evolutionary relationships based on the perhaps reasonable assumption that these are more conserved than nuclear DNA, so you may want to look there, if a molecular phylogeneticist doesn't weigh in with a better answer than I can give. This article seems to contain a good discussion of the issue: http://www.ncbi.nlm.nih.gov/pubmed/11158372