Of course the much older vintage team sets will be very difficult if not impossible to get, but I think a reasonable goal would be to at least get all the team sets from 1950 to 1971 for the Senators and for the Nationals 2005 and up. The main goal will be the flagship Topps, and Bowman sets when applicable. For the Nats I'm not sure about trying Upper Deck and Panini or whoever else has been in the game these last few years. Of course I will try getting Senators cards from before 1950 but I doubt I will be able to complete too many of those earlier sets.
I am working on a "Page" for my team set needs. On that page I am listing the sets by year with a tally of the cards I have from that set (ex. 10/12). My first few posts will be general decades, and then as I complete sets or get closer to completion I will post about them individually. My 1950s Team Sets List Post is almost ready to go.
1959 Topps 397 Washington Senators Team Card
One of my sources for compiling these lists is The Trading Card Database. It isn't completely flawless, but it thankfully helped me with a big portion of the listing.