New to genes, and have to read literature to find candidate genes for a particular study. I cannot for the life of my understand if all genes are placed into either the "nuclear" or "mitochondrial" category...are there more categories? Some are easy, like cytochrome subunit genes are always written as "mitochondrial" and then rhodopsin are written as nuclear...but other genes like ATPase etc. don't have those descriptions. When I search online further, it still does not clarify, so I am wondering now if there are just more categories to this?
I have limited my answer to refer to humans, but the advice generalises to other eukaryotic cells.
In human cells, almost all of the genes that code for proteins are located in the genome, which is located in the nucleus. The mitochondria have their own genetic material, however, the mitochondrial genes only encode for 14 proteins. The answer to this question also notes the existence of extrachromosomal circular DNA. There are also a number of proteins (1192) that are verified to exist but their genomic location is currently unconfirmed.
In your comments you mention ATP1 and note that it is
called a membrane protein. The gene is located on chromosome 19 in the nucleus. The protein, that is encoded by the gene, can be found in a variety of places, including the nucleus and also the mitochondrion. The gene for Cytochrome c oxidase subunit 1 (CO1/COX1) is encoded in the mitochondrial genome and it localises to the inner membrane of the mitochondrion.
The links in this answer all point to Uniprot. This is what I use to get an idea of the basic functions of proteins. The database includes information genes but its primary purpose is to describe proteins and their functions. The information is roughly correct, it is not perfect. It includes a many species and links to a number of tools, including the gene ontology which attempts to characterise proteins using a controlled vocabulary.