Q:

What should the root of a syntax tree be labelled with?

I am interested in understanding these structures work.  My question is: Why do some diagrams start with S, while others begin with TP, IP, etc... Is there a way to stick these all of these phrases under S?  Please use simple feedback, I haven't taken any linguistic courses in 10 years.

A:

Edit: This answer focusses on mainstream generative grammar approaches which are heaily based on English (or Indo-European languages') syntax, assuming that this is what you are primarily interested in. However, as WavesWashSands pointed out in their comment, things might look completely differently for other languages where the assumption of something like a category I is of not much avail and S might indeed be approriate.  
S as the root of a sentence is a rather old assumption that is rejected my most modern linguists and is only used for simplification when a detailled analysis of what a sentence constitutes is not relevant (e.g. when explaining how phrase structure grammars work in general, or in very simple "toy grammars" to demonstrate parsing algorithms in computer science/NLP).
When not immediately related to natural language syntax, but for the description of formal languages (such as {anbn : n ∈ ℕ}, i.e. the language consisting of all possible sequences of aaaaa...bbbbb... where there are just as many a's as there are b's) with phrase structure grammars, which has its use mostly in computer science and mathematics, S is still the convention for the root label, but usually thought of as an abbreviation for "start symbol" rather than "sentence".  
The reason why S is not so nice is that it doesn't really give any information of what it is built from, and doesn't fit the general scheme of constituent trees.
In X-bar-theory, variants of which pretty much any major syntax theory is based on, you want to build up your trees systematically starting from lexical items (words) below and making constituents larger and larger, going over to phrases until everything is combined to one maximal structure, thereby assigning every node a combination of a category (such as nominal, verbal, prepositional, inflectional, ..) and a so-called projection level (roughly, it tells us how complete our tree is up to this point: is it a single word, a phrase (= a group of words which somehow belong together) or something in between) encoded in the label name.
Labelling the root of your syntax tree with an S doesn't fit into this scheme now, because you do have "S" as an abbreviation for "sentence" and thus a kind of category, but it doesn't tell us anything about the mentioned projection level and isn't build up of anything S-like either (a CP (= complementizer phrase) has a complementizer in it, an IP (= inflectional phrase) contains an inflection node, ...); for all the other constituents further below in your tree, you have a so-called head which determines the category of the phrase, dependents which complement the head and so on, but the S is just standing there as a single S-thing and branches into, e.g., some NP and VP which violates the assumption that sentence structures are built up in sysetmatic and preditable patterns.
TP, IP, CP etc. are different here; they do fit the widely accepted X-bar scheme and give us the information we want, namely of what category a sentence is (something tensed/inflected/...) and the projection level (namely a complete phrase that can stand on its own). That's the reason why most modern syntax theories rely on these labels as the top nodes of sentences, because they don't break the general explanatory pattern of how constituent trees are built up.
Additionally, IP and TP are labelled so because they are headed by a category "inflection"/"tense" which makes sure that the sentence is properly inflected w.r.t. tense, subject-verb agreement and so on, and it is assumed that this happens at a stage higher up in the hierarchy after all verbs have started off as uninflected. If you don't include an I or T in your tree, but simply say that an NP and a VP combine to an S, the question is where the inflection comes from, because it must be reflected in the tree somewhere.
So, no, you can't simply put everything under S without violating basic assumptions shared by major syntax trends. But you can, if you want, make the generalization for yourself that "CP", "IP" etc. are more or less equivalent ot "sentence".    
TL;DR  

old syntax theories or dummy grammars without a need for linguistic
adequacy --> S  
more recent syntax theories that in some way make
use of X-bar theory and want to describe syntax in a more accurate and more generic way --> TP/IP/CP/...  

Edit: Two more comments:  

You write in your title "the head label of trees". The term "head" is not quite right in this context; it usually refers to the head of a phrase as assumed in X-bar theory, but apart from that it is not a term that is defined for trees as mathematical objects independently of a syntactic theory. What you mean is the root of the tree.  
If you choose to label your root with IP or similar, you can of course not just go and replace S by IP, but as soon as you decide to stick to consitent X-bar labelling and an account for inflection (which would be the motiviations for chosing IP, or TP or whatever), this labelling must be licensed, i.e., the category I must occur in your tree as the head of the inflectional phrase, so you'd need to restructure your whole tree accordingly. A tree of the form [IP [NP VP]] is not better (in fact even worse) than a tree [S [NP VP]] if your IP isn't made up of anything that involves the category I, similarly with T and C; so you actually get different trees depending on the choice of the root label.

