I just started with my course in genomics and I'm working with domesticated animals (cows, chickens, pigs, etc) and I would like to know which methodology is better to trace the process of domestication since the origin of these species. I'm thinking of using SNPs of a particular gene to identify punctual traits that were selected, but also I was suggested to do a complete screen analysis and identify all the polymorphisms present in each variant and compare them with the species that gave them origin.
Yes, everyone use SNPs today for such analysis. Some RADseq is probably the way to go.
Detecting selection is not an easy task as many technics exist which differ by their assumptions and by the applicability. You should probably try to find papers having done the same type of analysis with the same types of data and eventually talk with authors. Your lab might already be experienced in such analysis.
What test to detect genomic signatures of selection? might help but the suggested algorithms are mainly for the analysis of within species variation. Procedure like mcdonald-kreitman test and other more advanced methodology to detect selection over a phylogeny (such as OUWIE if you have phenotypic traits) might be of interest. You could also simply use some rank tests when having many independent domestication events. The exact methodology you end up using very much depend on your data (how many independent domestication events do you have for example, do you have phenotypic traits, ...).
compare them with the species that gave them origin
Do you really have sample of the ancestor? Most of the time people simply consider a non-domesticated descendant of the non-domesticated common ancestor. Don't make the mistake of considering an extant lineage as if it was a descendant. This extant lineage evolved too!