Coming from Vienna, you could take the Orange Line to the Capitol South station and walk. That way, you would not have to fight the zoo when transferring at L'Fant Plaza. You'll get a seat because you're at the beginning at Vienna. If you walk balk to Capitol South after the game, you'll easily get a seat then as well.
I don't care about the seat. I just take Metro every day and, well, I don't like it. I'm wondering if it might be faster to drive.
I almost always park in HH. It's a bit convoluted to get in and out, so look at the directions on the website and maybe take a look at google maps satellite view, but you miss all the traffic right at the park and it's only $5 or $10. About a 15 min stroll to the park.
Is there a map or something with these lots marked off? I distinctly remember seeing one at one point.