Alright, here's that overview on kinship terms for conlangs I promised. Keep in mind this is just fodder for ideas, and is not meant to be exhaustive: Just because I don't list it here doesn't make it impossible or even a bad idea. Many phenomena occur in natlangs that I don't cover here, but this overview does cover the really common stuff.
Firstly, some standard abbreviations used in the study of kinship terms:
E - Ego (the "deictic center" in the kinship term system)
B - Brother
Z - Sister
S - Son
D - Daughter
F - Father
M - Mother
These abbreviations can be combined as such: FZ = Father's sister, FZD = Father's sister's daughter.
Here I will focus only on the kinship terms of those who are only one or two generations of distance away from Ego, as these are the terms most likely to be non-derived. There are patterns and interesting going-ons in terms farther out on the generational tree (grandson, second cousin) but these are generally derived from the closer kinship terms in some way. Not only that, but more distant terms receive much less study, so I have less to say about them. A specialized construction for kin of 4 or more generations away will receive extremely rare use, and will likely be forgotten and replaced with phrasal constructions. Specialized non-blood kinship terms (son-in-law, half-brother, godfather) will be ignored for identical reasons.
Firstly, there are languages which have no distinguishing of kinship terms at all aside from generational. All female adults of a generation above you are called "mother", all females a generation below you "daughter", and so on. This system is common in polynesian languages. Keep in mind that just because there isn't any linguistic differentiation doesn't mean there isn't behavioral distinctions. People in these societies still treat their parents differently from unrelated adults, and their children differently from unrelated children. This goes for all term conflations, really.
Secondly, not all languages use these types of gender distinctions. Some languages rather than using absolute distinctions of male and female, instead use "same sex" and "opposite sex." I know of systems which use this system for same-generational terms (so a male sibling is called differently depending on whether you're male or female), but none that use this for extra-generational terms (same-sexed child, different-sexed child, etc.). Not to say this is impossible, however. For the current guide I'll ignore this and give attention only to the more common, absolute gender kinship systems.
Kinship terms, as do general kinship systems, also have a concept of lineality. Here I call a language's lineality its "focus." Societal lineality and linguistic lineality are generally the same, but this is not always so. A language with a different lineality than the society that uses it indicates either a new language put onto an old society in the form of loans, creole formation, or even total linguistic conquest, or an old language that has undergone a recent societal change. For example, medieval europe was mostly bilineal. Although the west is patrilineal now (recent fads notwithstanding), the languages of europe are still bilineal.
There are four main types of focus that can be distinguished:
Patrifocused languages tend to conflate maternal relatives and distinguish paternal ones.
Matrifocused languages tend to conflate paternal relatives and distinguish maternal ones.
Bifocused languages tend to not bother distinguishing between maternal and paternal kin and treat them both the same. Any conflation patterns present will affect both sides.
Afocused languages don't have a defined focus because they have little to no conflation. These could be interpreted as a type of bifocusing, but I find the distinction between systems like that in Turkish and that of modern English very useful.
Regardless of focusing, more distant terms are always more likely to be conflated than closer ones.
Modern English is a prototypical example of bifocusing with few other conflations (the only others being the conflation of male and female cousins). Take the following list:
Mother - M
Father - F
Uncle - MB, FB
Aunt - MZ, FZ
Brother - B
Sister - Z
Cousin - MBS, MBD, FBS, FBD, MZS, MZD, FZS, FZD
Son - S
Daughter - D
Niece - BD, ZD
Nephew - BS, ZS
Afocused kinship systems, by contrast, have up to 8 terms where English only uses "cousin."
To wrap this up, here are some common conflation patterns in languages:
1. The conflation of different-sexed siblings. Turkish does this with its cousin terms: FB is "Emme" while FBS and FBD are both "Emme Usaki." Unfortunately I don't know a good vocabulary term for this, but you see it everywhere.
2. Bifurcate Merging is the conflation of siblings with parallel cousins, and of parents with their same-sexed siblings. This merges M and MZ, as well as Z and MZD.
3. Skewing is the conflation of same-sexed relatives across different generations. For example, the merging of FB and FBS.
As an example, here's a patrifocused kinship system with partial bifurcate merging and skewing of maternal relatives:
numasa - F, FB
kumi - FZ
sina - M, MZ, MBD, MZD
puta - MB, MBS, MZS
taku - Z, FBD, FZD
nanuka - B, FBS, FZS
kimi - S, BS
nipa - D, BD
kamu - ZS
sita - ZD