I may choose tailed cecilians since they are the most primative of those and thus most closely related to the caudates.
In taxonomic and phylogenetic terms, that statement is logically...wrong. If an organism is more closely related to caudates than to caecilians, then it is by definition, not a caecilian. You're talking about symplesiomorphies, which are features shared by coincidental lack of change rather than by shared exclusive ancestry [synapomorphies]. In other words, all caecilians have a tailed ancestor, so the presence of a tail does not indicate a relationship with any outside group.
This particular example however, is a very bad one, as it is a subject of ongoing debate, doubt, and major differences. Most analyses place frogs closest to salamanders as closely related groups. Some, but few, studies place salamanders closer to caecilians than to frogs. A very few studies place salamanders and caecilians together and not related to frogs at all. Another small number of studies find salamanders and frogs together, but caecilians with a separate origin. This is a very problematic area, and a good example of the classification differences between living and fossil species. Many of the fossil classes/subclasses of amphibians are not mutual clades, but are actually nested within one another, with differing subgroups becoming dominant and distinct over time. Therein lies the Lissamphibia problem: do they all derive from a single ancestor within the aistopods or the broader temnospondyls, or do they derive from different groups of Temnospondyli, Aistopoda, or Lepospondyli? If they derive from different groups, they cannot logically be included in the same modern taxon together.
If that particular example is of special interest thought, just google "lissamphibia origins" and you'll find plenty of information. Regardless of origins and relationships, Ichthyophiidae is universally the most basal caecilian family, and all recent research identifies only a single genus
Ichthyophis, with
Caudacaecilia as a synonym.
Coming back to this...
I am looking less at who gets put in a category than the relationships of those divisions.
Content within the divisions affects relationships between them, and vice-versa. That's a major driving factor in recent revisions. Former "
Colostethus" were members of multiple unrelated groups. Former concepts of Typhlonectidae and Scolecomorphidae were within the former Caeciliidae, which was corrected either by dividing the latter or synonymizing the former two. Former "Ranidae" was a massive group which should have included Mantellidae, Rhacophoridae, Hyperoliidae, Arthroleptidae, etc etc; former "Leptodactylidae" similarly should have included Hylidae, Dendrobatidae, Centrolenidae, and more. Relationships within these groups was precisely what forced them to be divided up to accurately reflect between-group relationships. Likewise for former "Pisces", "Reptilia", and possibly for Lissamphibia as well.
For your specific example regarding limb loss, I think you need to look at both other living taxa and the fossil record. Limb loss and reduction is exceedingly common within and between groups:
Skinks - occurs within genera, between genera, and between families
Geckos - occurs between families
Lizards in general - Dibamidae, Acontiidae, Pygopodidae, amphisbaenians, and snakes all obtained limblessness independently. In addition, elongation and limb reduction has been obtained in Gymnophthalmidae, Diploglossidae, Anguidae, Anniellidae,
Lanthanotus,
Lerista, Scincidae, Lygosomidae, Sphenomorphidae, Cordylidae, Gerrhosauridae. Some living amphisbaenians have functional limbs, some living snakes have limb remnants, and there are fossil snakes with legs.
Whales - living taxa have greatly reduced hing limbs, while fossil taxa have differing degrees of limb development and body elongation.
Salamanders - Sirenidae have no hind limbs; Amphiumidae have reduced all limbs
Caecilians - at least one fossil has limbs
Stem amphibians - many examples of elongate and limb-reduced species.
Limb loss, elongation, and features generally related to neoteny/paedomorphosis have long been problems for classification, as they are frequently derived independantly due to evolutionary pressures, rather than being due to shared ancestry.