Nancy: Yep; you're on the right track. There are nifty tools that can help you keep track of the effort to align segments from your autosomal matches with your paternal and maternal lines...and their paternal and maternal lines. Tools like DNA Painter and Genome Mate Pro. If you haven't already, I'd surf around sites specializing in use of DNA information with adoptions, like DNAadoption.org. In general, working to identify biological family with autosomal DNA is less complex than trying deep dives back to, say, 5g-grandparents.
Mitochondrial DNA--which isn't part of the human genome at all--was the first type to be fully sequenced, and really the only kind up until relatively recently (as in the last decade) used to test ancient remains. The simple reason is that the tiny mitochondrial DNA molecule (only 16,569 base pairs all told, compared to the smallest human chromosome, number 21 at 48 million base pairs) was easy to sequence, and because each human cell (except red blood cells) have scores or even several hundred mitochondria in them...you have over a quadrillion mitochondria in your body. That makes for a lot of copies to test if some are damaged; ergo the usefulness in looking at ancient remains before HiSeq testing started taking over that realm circa 2014. Now mtDNA testing of ancient remains is a backup plan only, seldom the first type of sequencing attempted.
Point being, mtDNA is extremely valuable if trying to disprove a specific hypothesis, but not so useful genealogically at proving a hypothesis or randomly finding matches to unknown cousins. Because the mtDNA molecule is so tiny--yet has half as many coding genes as the Y-chromosome that comes in at about 58 million base pairs--there simply isn't much room for mitochondrial DNA to mutate. Even with an exact match on a full-sequence test, FTDNA gives only a 50/50 probability that you share an ancestor within 5 generations...and a lot of very bright people, like Dr. Ann Turner, believe that probability is way too lenient based upon numerous scientific studies of mtDNA mutation rates.
That's why mtDNA for genealogy can be misleading. Living DNA and others tout that they're identifying your maternal line, but in fact they're only testing select SNPs in order to arrive at a solid estimate of your haplogroup. That's great information, and it can tell you definitively that you don't share an ancestor with someone else; but it can't provide any meaningful evidence that you do share an ancestor in the genealogical timeframe.
The math there is pretty straightforward. The keeper of the mtDNA phylogenetic tree, phylotree.org, where all the haplogroups are cataloged, has just over 5,400 "nodes" defined in their most recent Build 17. A "node" is a defined ancestral haplogroup. For example, H4a1a1 is a node, and so is H4a1a2.
If you assume 5,500 mtDNA nodes, and a global population of 7.6 billion, you'll see that there are almost 1.4 million people for each mtDNA haplogroup. Really common ones like H2 will have many times that number, and very rare haplogroups will have markedly fewer. But still, the population of San Diego, California, is 1.39 million. So knowing your mtDNA haplogroup--even if it's refined down to the level of H4a1a1--would still be the equivalent of saying you've established DNA matching evidence to someone simply because you both live in San Diego.
Heck, as of three weeks ago mitomap.org had 46,092 mtDNA full-sequences on file, likely second only to FTNDA. Even if each was a unique haplotype, each would have about 165,000 exact matches (averaging) in the world. And if you want to add a real kicker to that, the modern human mitochondrial genome and the Neanderthal mtDNA genome differ on a total of only about 200 base pairs. That's how slowly it mutates and how little variation there is among humans.
Sorry for the digression. Something of a soapbox issue. Bottom line, though, is that autosomal DNA is always the best first testing choice if you're just seeing what you can see or if you're looking for close relatives. Both yDNA and mtDNA--unless you just want to spend the money out of curiosity--really require going into the testing with a plan and with hypotheses in hand. The yDNA and mtDNA haplogroups that 23andMe and Living DNA provide are only afterthoughts because the microarray testing chip they use, the GSA chip from Illumina, tests some yDNA and mtDNA SNPs by default and can be programmed (customized) to test for a few more. It's one testing pass on one microarray chip; they don't do for-purpose testing like FTDNA or YSEQ, for example. The 23andMe and Living DNA tests can provide a haplogroup estimate that's very accurate, but doesn't tell you much genealogically speaking.
As you can no doubt tell, though, it's all cool stuff to me, so I test everything I can test. Except full-genome sequencing. Not quite ready to shell out even $1,200 for that yet. I will once it's under $1,000 and becomes more popular..and somebody figures out a way to manipulate the massive raw data files for matching and comparison.