I would answer your question with more questions to you
1) Where do you think you will be doing your near-future diving?
2) What type of diving will it typically be?
3) What direction would you like to go with your future diving, if you know?
For example, my answers to those same questions when I started were as follows:
1) Florida Keys
2) Shallow reefs
3) No specific location or type of diving, but I would like to get my personal dive skills (buoyancy, trim, propulsion) up to snuff
For my three answers, there was no real reason to take Nitrox. When I did (eventually) take Nitrox it was for a specific purpose: My buddy wanted to do some wreck diving (which, in the area we were diving meant dives where Nitrox would be advantageous as compared to air), and so I took Nitrox in addition to some wreck/deep training.
That's not to say it would ever be "bad" to take Nitrox, but since you are on a budget, you might not want to take it "automatically."
Slightly off your topic: I would check into the AOW class and find out more specifics. I found that while it was fun, it wasn't necessarily the best value-for-dollar I could have had. I think that varies with instructor, so don't take my experience as gospel, but more as food for thought.
Blue Sparkle
PS: Thinking about your post further, I think it would be interesting to ask the LDS why they "want you to take Nitrox this winter." Their answer may help you to know what their reasoning is, and whether or not you agree with it. Reasons I could think of:
1) You plan to do some diving where it would be specifically preferable to air.
2) You have some reason to want to dive Nitrox on air tables for conservatism (health? or?)
3) There is another good reason that they know of (but for some reason they are not sharing it with you so that you can understand it...?)
4) They just want you to take a class and "stay active" with them, and they're tossing it off because it's a good progression for them, and not necessarily the best choice for you.