I've been a Buddhist since I was 13 years old, ever since my confirmation and studying the bible following that, realizing that I didn't believe in the scriptures which I was raised on then I started searching for some sort of a philosophical structure and knowing that without religion I'd have a void within me. To make long story short, I studied the tenets of Buddhism and the eight fold path and I started living like that at the best of time however strafing away from it at the worst of times. However I would like to add some depth to my understanding of Buddhism and it's teachings, however the local temples are either Thai Buddhists with the golden statues which I find revolting or the Zen which I'm not quite sure of.
As far as i can tell the delineation of school/sect doesn't really come into play until one plans to join a community for the long term or is in a doctrinal discussion.
The various schools have collections of texts, some doctrines therein are non-negotiable whereas a lot of texts will be in a "maybe true maybe not true" category (ie commentary) and the various positions in regards to those will be tolerated within that school as a whole, although some sects within a school might hold strongly a position regarding a particular non-canonical text and be thus closed off to those of other persuation.
Buddha himself said that he taught the doctrine of analysis (Vibbhajavada) and one would historically have ie Vibbhajavadins of Theravada, people who would reject some positions held within a school, based on analysis and cross referencing with texts known as true.
Nowadays there are different sects within Theravada, some reject the Abhidhamma, some reject commentary, some rejecting some commentary, some not rejecting anything at all even if the texts contradict themselves.
It is my impression that relatively few people actually study the texts before joining a school.
More often than not people find a community and get taught as the teacher was taught. More often than not the expression and methods are more or less based on the very recent popularizations or passed down tradition.
There is really no reason for having to choose a school before having familiarized oneself with the various doctrines.
Birds of feather flock together, so it is with holymen and views. If one wants to join a community one will for the most part have to learn their particular doctrine because it's just a lot less conflict if all members believe same things. The actual study of texts will often be neglected as well, because that's looked at as a bit dangerous as it might cause disruption and challenge the guru's authority.
Also most monks and lay people alike don't really study beyond the things their teachers tell them. This in part has to do with the sheer volume of essential and non-essential material to study.
If mastering a teachers expression & it's meaning takes 1000 hours, that alone might keep one occupied for years and it might not even result in any understanding of the essentials of what the Buddha taught but instead be based on stories, anecdotes, popularizations and new age systems of doing and explaining things.
Therefore you probably don't belong to any particular school. Ideally one should know why one belongs to a particular school and the various points of controversy.
You can frequent the various communities as you like and as i said people usually don't care about what you believe lest they see you as a threat or consider you for long term cohabitation.
There are a number of Buddhist schools, mostly falling under the umbrella of Theravada, Mahayana or Vajrayana. Well, Vajrayana is technically under Mahayana too. Zen, Pure Land and so on fall under Mahayana. Tibetan Buddhist schools mostly fall under Vajrayana. You can read about them in Wikipedia and also answers on this site for e.g. from this question.
You don't need to choose a sect or school now. Just start observing the five precepts (as best as you can - no pressure) and then become familiar with the original teachings of the Buddha, i.e. as close as possible to the Early Buddhist Texts (EBTs).
The texts which are as close as possible to the EBTs is the Pali Canon, also known as the Tipitaka or Tripitaka, which are composed of three collections. The collection known as Sutta Pitaka, contains the teachings of the Buddha, known as suttas or discourses.
The suttas are very huge. I suggest reading an anthology of selected suttas like "In the Buddha's Words" by Bhikkhu Bodhi. You can also find them in this answer. You can also use AccessToInsight's "Path to Freedom: A Self-Guided Tour of the Buddha's Teachings".
The sect corresponding to the Pali Canon is Theravada.
However, after reading the sutta anthology, you can then explore Mahayana teachings and texts, of course.
In any case, you don't have to commit yourself to any school or sect.
Through study of the teachings, you will improve your Right View. From there, you can decide where to go next.
One important thing is not to judge or decide what Buddhism is, based on what temples look like or what some Buddhists practise or what some teachers teach. Rather use the Buddha's words directly.
For e.g. you won't find any use of statues or idols, or the practice of chanting, or the use of amulets or mandalas or prayer beads or incense in the Buddha's original teachings. These things come from later cultural influences.
Another interesting thing is, in DN 2, the Buddha prohibited monks from practising astrology, palmistry, divination etc.
You don't have to join a sangha to be a buddhist, but it helps.
If there are sanghas nearby in your community, i'd suggest giving them the benefit of doubt by meeting the followers and learn about their teachings. When you're acquainted enough you will have an informed opinion to decide whether to stay or move on.
I think monks are ordained by other/existing monks. This history is called a "lineage". The world is big, over time the lineages in distant countries might have evolved into so-called sects.
I suspect that a layperson may belong to a "culture" (e.g. you might be born Thai or Vietnamese), and/or you can aspire to study any aspect of Buddhism from any tradition that's available and seems useful to you. I believe that even monks, ordained into one sect, might learn from others (yet still remain a monk). I'm pretty sure that some of laypeople on this site have studied more than one tradition (more than one teacher).
I think there's a sutta which warns against being too sectarian: Ud 6.4 includes the parable of the blind men and the elephant.