Hi, Nikki. Since your mother is living and willing to take a test, this gives you a big advantage toward your goal. You're absolutely correct to make your mom's test the next priority after your own. Like Jana, I tend to steer folks toward Family Tree DNA if there is no preference or reason otherwise; this simply because they store the samples submitted and new tests and upgrades can be ordered years later against that original sample.
However, I'd tend to stay with Ancestry for your mom in this case. Your autosomal DNA test looks at defined places, loci, on your chromosomes called SNPs (single nucleotide polymorphisms, pronounced "snips"). Not every testing company looks at the same SNPs--for example, new 23andMe and Living DNA tests examine only about 23% of the same SNPs as your Ancestry test--and to get the two to compare requires some mathematical smoke and mirrors called imputation. A brief explanation of imputation is at this blog post from last Wednesday; scroll down a couple of paragraphs to find it. But the message for you and your mother is that it's best that your two test results compare one-to-one as closely as possible: the more tested SNPs you have in common, the better.
Which leads me to the next steps with those two sets of results. You'll download the raw data files for both tests (that's done through the AncestryDNA user interface; it's easy to do) and then you'll want to create one account at GEDmatch.com--you can manage multiple kits from the same account--and upload the raw data from both tests there. GEDmatch is free to use for it's basic tools, and those give you arguably a better set of autosomal DNA features than any of the testing companies.
One of those features is called Phasing and it will give you a two-click way of creating a simulation of your father's genome--a "pseudo-genome," if you will--that establishes a new kit number under your account which you can then use to run matches and comparisons against, just like your and your mother's kits. I know it sounds slightly creepy, but once again it's only math. What this single-parent phasing attempts to do is identify what SNPs you did not inherit from your mother and use that information to create the new missing-father kit.
The new kit won't be a perfect simulation of what your father's results would have been if he had been able to take a test himself. That's because the DNA tests can't determine which allele you got from which parent at any given base pair, or locus. For example, let's say at one locus your test results show the paring guanine (G) and cytosine (C); and your mother's results also show a G and a C at that locus. Which one came from your father? There's no way to tell. Your father might have had either GC, GG, or CC at that locus in his results, so there's really no way to make an informed guess with any accuracy. The end results is that the new "pseudo-genome" will be comprised of significantly fewer SNPs than your original one, and the more tested SNPs you and your mother have in common, the more can be accurately included in the new simulation.
The result won't be perfect, but it certainly will be good enough to do its job: helping you determine which aunts/uncles, nieces/nephews, and cousins match your mother's side of the family, and which match your father's. I know this isn't exactly the question you asked, but the real goal of genetic genealogy is growing a base of strong evidence to aid in the evaluation of current and future DNA-matching scenarios. I'd personally put the words "confirm" and "prove" in the use-seldom file. DNA is just like any other evidence for genealogy: everything falls somewhere on a sliding scale from "absolutely true" to "absolutely false or irrelevant" and has to be scrutinized on a case-by-case basis. With autosomal DNA, for example, a match to a hypothetical 5th cousin will require a lot of detailed work and amassing of additional evidence in order to be considered strong evidence, whereas a match with a 2nd cousin is easier and more straightforward. And as with that possible 2nd cousin you just found, the evaluation of the DNA evidence goes hand-in-hand with the genealogical, paper-trail evidence. Since we can't test deceased ancestors, we have to rely on DNA matching with contemporaries...and that means getting back to earlier generations requires a solid paper-trail to complement the DNA evidence.
With you and your mother tested, I'd set Priority 3 at one of your brothers. That would do two things. First, it would corroborate, as full DNA siblings, that you both share the same mother and father. That would give you the ability to set the WikiTree status of your father's profile as "confirmed with DNA." Second, with that validation, should you decide in the future to have your brother's Y-chromosome tested for a deeper dive into your patrilineal line, you have the objective substantiation that you are, in fact, testing the correct yDNA. If both your brothers also have their atDNA tested, that opens up a new avenue called "visual phasing" uniquely available (mostly uniquely, anyway) to a family that has three full siblings tested. That's an advanced technique that would be down the road in your research, but you can Google it if you want some background on it.
Just because I said that a brother would be Priority 3, don't hesitate to broach the subject with your aunts and uncles when you visit in May. When it comes to DNA, the more the merrier! :-) The general adage is test older relatives first so that you don't lose the opportunity. And aunts, uncles, and half-siblings thereof are priceless because they're going to be a generation farther back than you are, and they will absolutely help you sort out which DNA comes from whom. A free tool you may want to explore to help you store and track that information is DNA Painter. From GEDmatch, you can copy-and-paste information directly into DNA Painter, making it fairly simple to use.
Bottom line is that the more data you have about closer family members (i.e., through 2nd cousins), the easier it will be to accurately evaluate matches from more distant cousins. Folks like Jim Bartlett who helped pioneer the use of autosomal triangulation routinely have triangulation groups of up to 20 DNA-tested individuals to help them validate a 4th or 5th cousin relationship. By nature, genealogists have a bit of Sherlock Holmes in them. DNA is a powerful new tool...not yet 20 years old, and the first autosomal testing for genealogy is less than a decade old. The more we dive into it as a form of evidence, the more addictive it can become. ;-)
