WES, almost certainly. First of all, the vast majority of phenotype-causing variants are found in exons. For most analyses that are looking into disease causing mutations, WGS is pointless. It only makes your analysis harder and doesn't actually add anything useful.
If you know you're interested in CNVs, that's different. CNV detection is hard in general but is particularly hard from WES data. Detecting CNVs in WGS data is much less error prone. However, you really should bear in mind that there are currently no 'good' methods to detect CNVs. This is a non-trivial problem and still in its infancy. While there are various methods that can detect CNVs, none of them find all (or even close to all). In fact, this is such a problem in the field that the currently accepted wisdom is that you should use multiple methods and combine the results. In fact, many recent CNV detectors do exactly that. And they still don't find all of them (especially not in WES data). Basically, CNV detection is not for the fainthearted and is certainly not for the non-expert.
The good news is that if you do have a disease causing mutation, it is very unlikely to be a CNV. It is far likelier that you're just looking for SNPs. Which brings us to the next issue. I'm afraid the algorithm you linked to, from what I can tell, won't help you at all. You're not trying to compare your gene to a list of healthy and unhealthy ones and figure out which group is most similar to what you have. First of all, because there are many differences (mutations) that don't actually have any effect whatsoever. These so-called synonymous mutations would still be counted by your algorithm but should be ignored. Second, because tiny differences can be enormously important. There are specific tools for what you want to do; don't try and apply broad, general mathematical approaches. You need algorithms that are specifically designed to deal with biological data and which take the underlying biology into consideration.
So, what you're looking for are programs called "Variant Callers". Two of the most popular ones are GATK and FreeBayes. These will read an input genome and compare it to a reference genome and give you a list of "variants", sites where the input differs from the reference. You then want to use resources like ClinVar or MutationTaster to check whether those variants are considered pathogenic. This is a bit of shameless self-promotion since I work for the company which created it, but VarSome, "The Human Genomic Variant Search Engine" is a new variant search engine that combines information from many different sources in a centralized and easy to search repository. I recommend it highly (and it is free).
However, before you get to finding your variants, you will need to align your genome to the reference. Basically, modern sequencing methods work by cutting the genome into many, many small pieces, copying each piece multiple times and then sequencing each piece. So the output of a sequencing run is a text file that looks like this:
This is usually several gigabytes (something like ~2-3G for WES and >80G for WGS). Therefore, the alignment of these sequences needs a powerful machine and you don't even want to try to align WGS sequences on your laptop. It will take weeks and will probably fail. Another reason why you should prefer WES over WGS for this. In my work, I routinely align WGS data to the reference genome and that can easily take >100GB of RAM.
The bottom line and what this rambling answer is trying to get across is that:
- WES is better than WGS when searching for disease causing mutations. It is far easier to analyze the data and 99% of the cases you want are in exons. It is also much, much cheaper.
- This isn't simple. You seem to think you can sort of waltz in and do it yourself. You can, but it is very far from trivial. It is also not cheap.
So, if you do actually have the money to pay for a WGS analysis (this costs several thousand euros/dollars, in case you didn't know), which is very surprising if you're just a private individual, instead of spending it on WGS, get a WES and spend your money on getting an expert to analyze your data for you. Seriously, this is what I do for a living, you really don't seem to have grasped quite how complicated it is. And no, I am not suggesting you hire me :). There are, however, companies that offer this sort of service. Use them, don't reinvent the wheel.
Useful review articles for CNV detection:
- Zhao et al. BMC Bioinformatics, 2013, 14(Suppl 11):S1 (DOI: 10.1186/1471-2105-14-S11-S1, link)
- Tattini L, D’Aurizio R and Magi A
Front. Bioeng. Biotechnol, 2015. 3:92. (DOI: 10.3389/fbioe.2015.00092, link)