Always like to sit on the third base side to watch the Yankees bench.  You never know what will happen in the dugout with the Yankees.  Tickets are always available for the right money.  My recomendation is set your budget and shop around.  I care less about the bucks and more about the seat location and the time it takes to get the seats I want.  I end up going the conciegre at the hotel I am staying at a few weeks before my trip and pay the premium to get what I want.  I unfortunately do not know when tickets actually go on sale.  Have a great trip and enjoy the stadium.

I agree with Bigfan above - if you have the $$, worth spending for the good seats.

Either way, go for the whole experience.  A few rec's:

1.  Go to a day game.
   
2.  Go early and tour monument park in CF - I think it's better than the Hall of Fame in some ways.  I get chills everytime I go out there - it's awesome.  
   
3.  If you can go to multiple games, spend one in the RF bleachers.  The "Bleacher Creatures" provide a completely different feel, and something to watch between innings.  Their "roll call" around the diamond is one of the most unique fan-player interactions in sports.
   
4.  Take the subway.  The 4 train (from the East side of Manhattan) or the B or D trains (West side) drop you off right across the street.  If you take the D, make sure it's an express - the local train doesn't stop at the Stadium.  Don't worry - going 1-2 hours before a game, and immediately afterwards - the train is packed with game-goers and very safe.  Adds to the experience.  Plus a lot cheaper than a cab, and none of the hassles of driving.
   
5.  Be careful wearing opposing team gear.  You can get away with it on field level (more expensive seats) but I'd be careful in the upper deck - and I definitely wouldn't do it in the bleachers.  You may be able to get away with a Rangers hat without issue (other than a "Rangers suck!" chant headed your way), but I've seen fights break out when a Red Sox fan walks in all decked out.

Bottom line - enjoy it.  It's a shame they're tearing the place down after the season - every baseball fan should see a game there, at Fenway, and at Wrigley.