Congratulations on taking your first cruise....we took ours in November last year. We booked Princess from Long Beach to the Mexican Riviera. For a first cruise it was wonderful. When I booked it I had no experience with booking a cruise. I took the advice of one of my friends who's been on almost 30 cruises. He referred me to Cruises Only. Jomari (1800CRUISES ext 82432). He walked me through the whole process, answered all my questions, got an excellent price, and gave me advice so that I could make informed decisions for all the little things when booking my cruise.
We too were on a budget, but I also wanted to make sure I chose the best cruise (picky husband) so that it would ensure my ability to persuade my husband to cruise again in the future. It worked, (I just booked our second cruise within 6 months for the end of May on the Elation out of San Diego). Here is my advice for you: When you choose your cruise make sure you're going somewhere you want to go and for the length of time you need to really experience what cruising is about (a cruise too short will make you feel your getting off when you've just got on). I believe the Mexican Riviera is a cheaper cruise for the 7 days, but if it isn't going to places you really want to see....is the price really worth it? I've read posts on this site for almost a year now and there is both good and bad about each cruise line depending on who you talk to. You didn't say in your post who you're traveling with or what your ages are. Your age and what you expect from a cruise (in regards to activities) is definitely something you want to take into consideration in choosing your cruise line. For example, when my husband and I took our first cruise (we're both in our 40's) we chose Princess because it was layed back, there was more pampering (like the little things, Fancy toiletries and such) and it didn't have too many children on it. However, this time, we're talking our daughter and her best friend (both 14), Carnival is the line we chose due to what others here on this site and Jomari at Cruises Only suggested.
Back to saving money....you can take bottled water on board with you. If you drink water you may want to do this. Bottled water costs at least $2.50 per bottle on the ship. I drank the tap water on the ship and found it to taste a bit like chlorine. If you drink alcohol, some lines offer a drink card (Carnival has one 4 drinks for approx $25.00 which includes the tip), beer by the bucket (5 for the price of 4), and of course there is the unlimited soda card. However, keep in mind that there is coffee, tea, lemonade, iced tea,milk, and other juices available for free 24/7 in the buffet dining area. Yes, it is a hassle to get it from there when you're busy doing something else, but it's free. Don't use your cellphone while on board...charges can be literally out of this world for calls, texting, and retrieving any voice mails you receive.
The cruise lines try to get you to spend money...lots of money. If you want to save money, don't buy the pictures the cruise line will take of you and your traveling companion. I think these pics go for approx $25.00 each. It's cheaper if you have someone else snap pics of you with your own camera. Some cruise lines advertise art auctions....these are very expensive and personally, I wouldn't waste my money or time. If you have your heart set on buying something (besides alcohol) from the ship, wait until the last few days or last day of the cruise. You will see advertisements for big price reductions at many of the stores on the ship. Another way to save money is to make sure you eat your meals on the ship. You've already paid for the food on the ship...your breakfasts, lunches, snacks, and dinners. Sure, it's nice to eat while doing an excursion in Mexico, but what if the food makes you ill? It could really screw up your vacation.
If you're really concerned about your budget, see if there is a way you can prepay on your ship spending account (Carnival has it). I am applying bits of money to my account each week, before we sail so that the final bill I receive will be very little if anything at all. I don't like surprises.
I am by no means an expert and things change all the time, but being a second time cruiser, I thought some of the things I found as a newbie, may be helpful to you. The more experienced cruisers on this site can provide invaluable information for you too, especially those who have already cruised all the different cruise lines.
Good luck on your cruise. I am sure no matter which line you choose, you will come back addicted to cruising!!