Additionally, are there any such things as hierarchies, where if I want to include one sound, I should also include another?
Most if not all phonemes in a language will share something with at least 2 other consonants. For example, if a language has a plosive, then it'll probably have several. Likewise, if it has a voiced plosive, it'll probably have other voiced consonants, possibly of other points of articulation.
Of course, this just the majority of the time. English, for instance has only one palatal consonant (the 'y' sound) and only one lateral (our 'l'). Though few languages have more than one lateral consonant (assuming they have any at all), and 'y' is the only common palatal consonant. All the others are rare.
There, however, a few universals. All languages have voiceless stops. They may only have one (and there are that do), but they will always have one. Also, all languages have monophthongs. So that means that there aren't any natural language out there that only have diphthongs for vowels. Note however, that diphthongs in a language can be made up of monophthongs that don't exist in the language. Take note that the English 'o' sound is actually a diphthong. English doesn't have the monophthong 'o' for some reason. This is why books that teach you foreign languages often tell you cut off the last part of the 'o' sound. What they're actually trying to get you to do is not do the off-glide that our 'o' normally has.
Beyond that though, there are no universals. No one phone is found in all languages. And exactly how many phonemes a language has varies widely. The most common is 5 vowels (the standard 5-vowel array you see everywhere) and 20 to 25 consonants. But there's languages with only half a dozen consonants, and others that have dozens. Then there's the case of Ubykh, which not only has dozens of consonants but only contains 2 vowels, which are of course prone to considerable allophony. In general, its hard to find languages that have fewer than 5 vowels, but they do exist. Several native languages up in Canada only have 4 vowels. The Semitic languages only have 3 vowels (well, modern Arabic also has 2 diphtongs, and its three monophthongs distinguish length, though classical Arabic only had 3 monophthongs, I don't know about Hebrew).
No, even among natlangs there are no true universal sounds. The closest would a low /a/ type vowel, which 98%+ of natlangs do have, but not all. Note that this is in terms of phonemes, not allophones. Other very common phones include the stops [p/b], [t/d], and [k/g], as well as one or more nasals.
When creating a conlang, a minimum of two to three vowel phonemes or three consonant phonemes (with more consonants if there are few vowels and vice versa) would be expected for a naturalistic phonology. The natlangs with the smallest phoneme inventories have on the order of around ten to twelve phonemes, however analyses of such languages are usually controversial. Such languages also often have tone or phonemic length, which does make it harder to compare languages and harder to come to consensus on what should count as 'smallest'.
In general, /t/, /k/, /m/, /n/, and /a/ are phonemes found in almost all natlangs (but certainly not all).