"$1,100 dollars in average for a flight-round trip. My question is if that's a good deal?"
It sounds pretty good to me. I paid $811 to fly from JFK to Madrid and Barcelona to JFK, in September 2015. Round trip to Barcelona on my dates would have been closer to $900 (I forget the exact price). And of course Los Angeles is much farther from Spain than New York is. That said, there is no longer much rhyme or reason to airfares. So, on to your next question:
"Where do you guys purchase your tickets at for flights to Spain?"
Most of us research multiple sites. We look at Kayak http://www.kayak.com/flights or Matrix ITA http://matrix.itasoftware.com/ or Google Flights https://www.google.com/flights/. We also look at the airline's websites directly. However, when it comes time to purchase, almost everyone will tell you to try to buy the ticket from the airline directly. That's because, if there's any problem, the entity that sold you the ticket is responsible; it's much smoother if it's the airline itself rather than a third party, particularly if the third party is some "ticket agent and roadside fruit stand" type outfit.
When doing your research, be sure to consider ALL costs. For instance, some budget airlines are now flying from the US to Europe, but you may have to pay for checked or even carry-on bags. If it's cheaper to fly out of Oakland than LAX, how much will it cost in time, money, and hassle to get there? Similarly, flights to Madrid may be cheaper, but don't forget to include the cost of getting from Madrid to Barcelona. I'm not saying you can't do these things, but just know what you're getting into.
One "budget tip" you're sure to hear sooner or later is to fly to wherever you can to in Europe cheaply, then pick up a budget flight (on Ryanair, Easyjet, Vueling, etc) separately. Be VERY VERY careful if you're thinking of this. You need to allow a lot of time for this connection and pray that everything goes smoothly, because when you have two separate tickets like in this case, if anything happens, you're stuck. And many of the budget flights are from different airports than the ones that get the transatlantic flights (for instance, flying from the US to London you'll land at Heathrow or possibly Gatwick, but many budget flights are out of Stansted, a huge distance from both of these).
Having researched your flights, you'll recognize a deal and be ready to pounce. Once you've purchased your tickets, don't look back (too crazy-making).
"How long does it take to get a passport?"
Anywhere from two to eight weeks (sometimes even more) depending on how busy the passport office is. Now is a great time, as it's before the rush (spring sees a huge number of applications for upcoming summer travel). Here's the official US government website: http://www.travel.state.gov/content/passports/en/passports/apply.html
Other websites are companies that charge extra money for doing what you can do yourself (unless you're in a real hurry, which you're not). It may take some for you to gather the necessary documents, so start now; this also means you can avoid the higher fees for expediting (you can get a passport in one day if you have proof of imminent travel, but it's going to cost you)
While you're waiting for your passport, a great thing to do would be to read Rick Steves Europe Through The Back Door. It will give you all the basic information you need to travel internationally - money tips, finding hotels, food, etc. Then, get and read Rick Steves Barcelona (or if you're seeing ohter parts of the country, Rick Steves Spain). Reading these books will answer questions you didn't even think to ask.
