I'd like to start programming in Scheme but the variety of different implementations is confusing. What are some advantages or disadvantages of various implementations?
Every implementation tends to focus on something different. Racket emphasizes its large libraries as "batteries included", while Ikarus Scheme touts itself as compiling fast code. You should examine implementations based on what you want. If you're just learning Scheme, DrRacket is a good choice with its friendly interface and specific environments for various Scheme books.
Also, you probably don't need to find a R6RS implementation, when most implementations target R5RS and most textbooks were written for R5RS and earlier.
Since you're looking to learn Scheme, I recommend The Little Schemer as an introduction to thinking using Scheme's lists and recursion.