You can get an all day Metro fare card for $14:
http://www.wmata.com/fares/purchase/passes.cfm , or use the Circulator bus (which is different from the regular DC Metro bus):
http://www.dccirculator.com/
Security into the Smithsonian is pretty easy-going. Since your bag is going through the xray, and you're passing through the metal detector, just tuck your granola bars and bag of trail mix in your back pocket (done outside, of course - I've seen people stand in front of the guards and pull stuff out of their bags, intending to carry it through the metal detectors [facepalm].)
Since you'll be on the mall and Capitol Hill, be sure to familiarize yourself with our quadrant system - Northwest (NW), Northeast, Southeast, and Southwest. The Capitol is the intersection of the quadrants. E.g.: The mall is west of the capital, so everything on the south side of the Mall is in SW, and everything north is in NW.
This will get important if you go to Union Station, which is on North Capitol Street, the dividing line. 14 blocks WEST, in Northwest is the Smithsonian American History Museum. 14 Blocks EAST in Northeast is ???? When I see tourists heading EAST on Capitol Hill, saying things like: "This is 4th street - only 10 more blocks to the Smithsonian", I always point out to them that they need to head in the other direction. Just check the street signs at intersections - they'll say 2nd Street NW or 3rd street SW, for example.