If you're not valuing options that are deep in the money (subject to early exercise), then any of these models are going to give virtually identical values. Unless you're doing big size, you can use Black Scholes, binomial, Bjerksund Stensland, Whaley (quadratic), or whatever and the difference between the theoretical prices they produce will be for all practical purposes irrelevant.
GARCH is a separate category; it is not used to compute implied volatility, rather, it looks back at price data and computes actual (historic) volatility. Any pricing model can be used to produce an implied volatility. You just keep feeding different volatilities (guesses) into the model until one produces the price for which you are trying to find the IV. That's all the computer is doing when it determines an implied volatility for you. You cannot directly solve any of these models for volatility.
http://www.dbquant.com/Presentations/BachelierConference.pdf http://www.maths-fi.com/article_Why...ption_Pricing_Formula_Haug_Taleb_nov_2007.pdf
I was attempting to learn these formulas for possible arbitrage of options (from studying options chains where a stock would not move and random options would rise 10%). However, as a small time trader, I don't believe I could delve into this yet. What do normal options traders use any of these formulas and models for, if anything?
Forget about arbitrage unless you can predict volatility better than the market. The important bit is predicting volatility to use in the pricing model, not which pricing model you actually use. Without good estimates it's garbage in garbage out!