Any recommendations for a very introductory text on Symmetric Polynomials?

The standard textbook reference nowadays is Stanley's Enumerative Combinatorics, Volume 2. Macdonald's monograph is the older, more advanced alternative. (Now that I look at it, these are the two real sources in freond1's link.) Stanley is a wonderful writer (perhaps a little dry for a non-specialist? really wonderful though!) and Macdonald is an excellent reference, but unfortunately these are not likely to be appropriate for you, and they're certainly not "very introductory". You might try glancing through Stanley just in case it's more appropriate than I expect. His is the most elementary exposition I'm aware of.

Honestly, Wilf's book is really weird--it's basically written for bright high schoolers, so it assumes incredibly little background, and very few math books have that target audience. Mostly these things are aimed at graduate students and above. That said basic symmetric function theory could be aimed at bright high schoolers, I just doubt anyone's done it. It's honestly a good idea since there's plenty of appropriate content (e.g. Young diagrams are friendly), it would serve to popularize algebraic combinatorics, and it would pair well with Wilf's book. Maybe I will someday--who knows?--though certainly not for years.

In a completely different direction, I recently discovered J Michael Steele's "Cauchy-Schwarz Master Class" book; you can read some sample chapters on his web site. It's really a work of art--it manages to be interesting to me mathematically (and pedagogically) while likely being appropriate for undergrads with minimal experience in real analysis. The exposition is geared towards equipping the reader with tools to find or prove inequalities so is based around "challenge problems", there are plenty of great exercises, and they all have worked solutions. It's probably ideal for competition prep.

Oh, for what it's worth, you might get better responses to these sorts of questions in a more advanced forum like Math StackExchange's community wiki.

Good luck. If you find a more elementary exposition than Stanley, please mention it.

I really don't know, but https://en.wikipedia.org/wiki/Symmetric_polynomial... lists a few. I suggest looking for those on amazon.com, and seeing if there are customer comments on those or other similar books. Reviews of math books there often discuss the level and clarity of the book, and make recommendations of similar books the reviewer likes. This looks like a very advanced topic, so there might not be a lot of comments on amazon, but there should be some.