I went to see the Spanish GP a few years ago, it was a good one.
I suggest grandstands G (you get to see most of S3) or L (you see T1/2 and T5/6). Main straight grandstands are more expensive, but since it your first GP you may also want to be there to see the live pitstops.
Upsides: seeing a GP live is always a great experience as you get a very different feeling from what it's like on TV.
Downsides: the race will likely have no overtakes at all.
During the GP itself, except watching the cars, there's not much to do... if you can get the live timing app at the same time, it helps follow what's going on (much harder than on TV even with the screens around the track).
It will basically take the whole day as there are support races in the morning (GP2, etc).
You can bring your own food, everything is quite expensive at GP venues and not particularly tasty.
If you have time before or after, the city of Barcelona (about 20km from the circuit itself IIRC) is obviously the main point of interest nearby, and it's really worth it (night life, monuments... depending on what you're interested in besides racing).