I'd appreciate any moderator or participant feedback on my approach (to make sure I'm on the right track).

Here's how I plan to best leverage the large number of autosomal participants on Ancestry.com to help with my Hamilton (paternal) surname research...

Testing strategy:

1) Take the Autosomal DNA 'Family Finder' test via Ancestry.com (done and the results are in)

2) Take the y-DNA test via Ancestry.com (pending)

3) Sponsor another person in my family tree to take the Autosomal DNA test. This person will be one who...
a) shares my Hamilton (paternal) lineage but not my maternal lineage.
b) is in the same generation as I am relative to our most recent common Hamilton ancestor.

Analysis strategy:

1) Identify high probability 'distant cousin' matches for the Hamilton surname that are present in both of the autosomal test results. Shared matches will increase the probability that a given Hamilton match will not be from my maternal line.

2) If we cannot find a family tree (paper trail) connection to these high probability paternal matches (matched from both our autosomal tests), then suggest and sponsor a y-DNA test with the matched Ancestry.com autosomal test participant to confirm that we in fact do have a paternal line match.

Summary:

The autosomal DNA test via Ancestry.com seems to be great for finding many possible family line matches in part because of the large number of participants (relative to the y-DNA test), but it is difficult to use for just paternal line surname research without a strategy such as the one above to use the autosomal DNA test results to narrow the leads for follow up y-DNA testing.