I'm about creating my first conlang grammar, I know a few general characteristics yet I don't truly know where or how I should start to outline it. I only have messy pieces of informations about. From your experience, what could you advise me?
It would probably be a good way to start with the features you want to express through grammar. Many features can be expressed in different ways, lexically, through morphology, or through syntax. For example, 'subject' could be done through a particle, an affix, or through the position in the sentence.
You first come up with the list of features, and then you look at the inventory of forms in the grammar. Do you want a complex morphology? English, for example, marks very few features through morphology (plural for nouns, 3rd person singular for verbs, tenses, …) and a lot through word order or by adding auxiliaries.
The inventory will define the shape of your language; you can also start with that and then assign features to it. But be clear what kind of features you want to be able to express – not every possible distinction needs to be expressed in language. Do you want to mark the gender of the subject in the verb? Perfectly possible, but probably not very useful, unless your language is for a very gender-segregated society.
Obviously, the more features you want to express, the more complex your grammar will be. As an extreme example, toki pona pretty much only uses word order and a few particles to distinguish between subject/verb/object, and ignores number or gender markers. In Esperanto most work is done by the morphology, which encodes the role in the sentence, gender of nouns, number, and even a range of semantic relationships (eg "room where you do a particular action").
It's probably best to start at broad strokes and clean up the detail later. The first question you should ask yourself is "Do I want to have an analytic, agglutinative, fusional, or polysynthetic language?" This will decide whether your language will be making sentences by putting a lot of words together in a specific order (like English or Mandarin), putting a bunch of affixes on a moderate number of words (like Korean or Navajo), putting a few very specific affixes on a moderate number of words (like Spanish or German), or stringing together a large number of component pieces to make a few very specific words (like Coptic or West Greenlandic).
Next, you should ask "Should my language be primarily head-initial or head-final?" A head-initial language will probably have Verb-Subject-Object or Subject-Verb-Object word order, put auxiliary verbs before matrix verbs (e.g. have gone), use prepositions (e.g. at home), put adjectives after the nouns they modify (e.g. house new), and mark the start of a relative clause. A head-final language will probably have Subject-Object-Verb word order, put matrix verbs before auxiliaries (e.g. gone have), use postpositions (e.g. home at), put adjectives before the nouns they modify (e.g. new house), and mark the end of a relative clause. Of course, as these examples show, you don't have to pick one exclusively, but nearly all languages are predominantly one or the other.
Third, you should ask "Should my language be primarily head-marking or dependent-marking?" A head-marking language will be more likely to use polypersonal agreement instead of case marking, mark possessa instead of possessors, and have adpositions that agree with their referents. A dependent-marking language will be more likely to have case marking, mark possessors instead of possessa, and have demonstratives and adjectives that agree with their referents. Again, you don't have to go all in here, but you should lean either one way or the other.
For these last two especially, it's very helpful to learn which word is going to be the head of a given phrase. For example, the head of a sentence is the verb, the head of a noun phrase is the noun, the head of an adpositional phrase is the adposition, the head of a possessive construction is the possessum, etc. These aren't really intuitive (at least to me), so it's best to just memorize them.
Knowing these three things right from the start will help you avoid some of the most common typological pitfalls that will make your language feel clunky to use. But choose carefully, because these choices will end up so ingrained in the language that it will be a royal pain to try to change them later. From here, you can move to making more specific decisions, like what grammatical distinctions you actually want to make, and how specifically you're going to make those distinctions.