What DNA has the most info for getting a person's likeness?
Except for Red Blood Cells, every somatic cell contains two copies of the autosomal chromosomes and a pair of sex chromosomes, either XX or XY (Assuming an average human being) One set is maternal and one is paternal
Some lymphocytes actually recombine their chromosomes, so their DNA will be functionally different to all of the other somatic cells in the body.
Gametes undergo Meiosis and will be haploid, only containing one copy of each autosomal chromosome and one of the sex chromosomes
Cells accumulate mutations over time. The closest you could probably come to an exact clone of a person is if you harvested one of the cells from the eight-cell stage of development. The other seven are able to go on and produce a viable and healthy person. The harvested cells DNA would be the closest to the DNA that combined in the fertilization of the egg. The next closest would likely be stem cells from cord blood. Then probably neurons, as they tend to divide the least.
As the link you posted said, ATCG can be represented in a two bit code, so for about 6 billion bases, you would need about 1.5GB of storage (You need to capture both sets of chromosomes in order to produce a person).


There are places where you could compress the data. Telomeres could be removed and just added back after the fact, as there is likely a standard length for each chromosome of the six nucleotide repeats. 
Though you could have a minimum of a two bit code, you would really need a larger data set. You would need metadata, so things like polarity of DNA and chromosome number. 
You might also want data about the alleles of each and every gene, that way any errors could be fixed. If you are making the DNA from a data set, there is no sense keeping any genetic defects or diseases in the sequence when you remake it.

Craig Venter, one of the protagonists of the Human Genome Project has a company that is able to produce synthetic DNA for a whole organism. They have reportedly produced a synthetic bacterium, so in theory, they could print DNA from a database and recreate an entire genome, though at what cost and how long I am not sure.
The Original sequencing of the Human Genome did cost Billions of Dollars, however today's sequencing machines can produce an entire genomic sequence more in the range of thousands of dollars. I am not sure if they have broken the $1,000 threshold yet.
Most of the commercial companies do not produce full genomes. They likely do not even sequence a full exome (The areas of all genes that make up the coding sequences of mature mRNAs). They likely do some form of polymorphism analysis to determine if for any given gene you have certain allele other than the Wild Type allele. In this kind of analysis, you do not really need a full sequencing to determine what gene a person has, you only need to identify areas of key differences to determine what is what. That being said, the data collected by a commercial genetics company would likely not be sufficient to recreate an entire genome.
Another important factor is Epigenetics. Just because you have the entire base sequence of the person, doesn't necessarily mean that synthetically creating all 46 of that person's chromosomes would give you the necessary material to transfer into an enucleated oocyte to then produce a new person. You would likely also want to capture the epigenetic encoding as well as the full genome. The epigenetic code that you would likely want would be from one of the cells from the 8-cell stage of development I mentioned earlier. While we have been able to clone adult mammals by nuclear transfer, those animals have had issues with cancer and premature aging. This may have something to do with telomeres, but it also may have something to do with the epigenetic code in early development.
There are other considerations in development as well. There is exchange of nutrients between mother and fetus during development. There is also a sharing of immunity and probably hormonal signals from the mother that can effect development.
Also women are mosaics. A woman would also have the added challenge that every single one of her cells has one of her two X chromosomes inactivated, so depending on which one is inactivated, at random, will determine which of the two X alleles she will be expressing in that cell. It is very possible that her clone would be different from her in appearance.


That is a pretty extensive list. I probably have missed some things. One thing I have definitely left out are all of the structural proteins of chromatin and how to package the DNA into a nucleus. We do not yet understand all of the mechanisms to compact DNA down into a nucleus, so we would have to answer all of those questions before we could figure out how to print and package the DNA to make a clone of a person from a database of their genome.

As we have not currently cloned a human, then it is difficult to say if it is possible. Things that we can do, even in other mammals do not always translate to humans and human cells. There would also be significant ethical hurdles to overcome and based on the current sentiments, it is unlikely, even if we have the technology, that society would allow human clones to be produced.