There are many wonderful guides for getting started in genetic genealogy. This is not one of them.
This checklist is for those who are serious about using genetic genealogy to bust down brick walls, who plan to avail themselves of all of those proper tutorials, and who just want to sort out their mise en place before things get rocking.
Are both of your parents alive and willing to test? Then test them, not you. They have twice as much ancestral DNA to explore.
Any grandparents alive and willing? Great-grandparents? Siblings of any of these? Run, run and beseech!
If you have to make decisions based on budget like the rest of us mortals, then begin with whoever is most likely to, ahem, not be able available for testing in the future.
Keep in mind that even if you test only one person, taking multiple tests is ideal. That said, it's better to have tested many relatives one way than to have tested one person several ways.
Be mindful that 23&Me's test also provides health-related information. Make sure your test-taker is fine with this. My husband wasn't, and so we fish in other pools. If I, greedy genealogy that I am, can handle this, so can you.
FTDNA is the only mainstream company doing "thorough" yDNA/mtDNA testing. They also store your DNA, so you can order one test now and others later without getting a new sample. If you think that you will want to know more about the test-taker's direct paternal or direct maternal lines, also test with FTDNA.
Not an American? Consider testing here. LivingDNA takes uploaded results from other companies (see next section), but the wait will be an unknown number of months, and you may or may not get all of the features you want (reports vary). American? Only if your budget is big and your patience is short.
Sales happen at all or most companies around DNA Day (April), Mother's Day (May), Father's Day (June in the US, September in Oz), and Christmas. Some companies, like Ancestry, discount their kits at other times, too, like St Patrick's Day. Google around or hit the various Facebook groups before ordering and see if a sale is likely to come up soon. (The $20 you save is $20 that you can put on another test...)
Don't withhold your family tree because you think playing coy will lead to more personal communication. I almost never contact matches without trees. I do reach out to people with trees when I have a discovery they might enjoy. I just don't have time to woo people who may not even care.
The presence of a tree signals that you are interested in family history (and not just ethnicity charts) and shows others what you already know.
If you have the time, work on adding as many cousins as possible using census and vital records. I have been able to quickly sort out countless matches with no obvious connection because I remember (or can quickly double-check) those collateral line names.
Attach a tree at every place where you've tested or where you've transferred results. You might rely on a link to another site at, say, FTDNA, but at least list your surnames so that the tools will work as well as possible.
Download your raw data from wherever your results come in first and transfer to the following sites. Do this even if you tested everywhere because it's the only way to see segment locations for Ancestry matches.
Genesis.GEDmatch.com: This is the only site that takes results from everyone. The tools here are powerful and ever-evolving. If you're an Ancestry test-taker, be sure to use a name that makes it easy to find you on the Ancestry site (and attach a tree for the same reason).
Be advised that GEDmatch allows law enforcement to upload DNA samples of victims and offenders alike. If you match, your family tree may assist in solving a crime.
MyHeritage.com: pretty interface, international customer base, and a promising "theories" tool that tries to predict how you're related to someone.
FamilyTreeDNA. Be aware that uploaded DNA tests can't be used for yDNA and mtDNA testing.
I love spreadsheets - I will use almost any excuse to make one - but I'd cry if I had to go back to using them for genetic genealogy. There's a learning curve with the above tools, especially GMP, but it's really worth it, even if you don't use all of the features.