My goal for the parser is that it should be very easy to do the kind of thing that you're talking about, so to whatever extent that it isn't, do let me know, so that I can fix it.
Alternatives include established lexers and parsers such lex, yacc, and bison (http://oreilly.com/catalog/9781565920002) which have a parser DSL (domain specific language, a mini-language devoted specifically to parsing). If you like regular expressions the grammar rules in perl6 are worth checking out. If you like your parser language to be programmable so that you can build complex parsers out of smaller ones in your own way, Haskell's parsec is a good one to look at.
I believe one of your primary tradeoffs will be speed vs. flexibility. If lex/yacc/bison will do what you want, then they will be among the fastest since because their parser language is limited, it can be compiled down to code that parses fast.
As you move up through the options of Perl, parsec, etc., and my parser, you gain programmability and flexibility at the cost of speed.
If know exactly what you want to parse, it makes sense to go directly to the fastest parser that will do what you want. If you're not complete sure, if you want to experiment, then from an exploratory programming point of view it makes sense to start with the most programmable and flexible parser library as that won't impose constraints of what kinds of things you can parse; and then, after you've figured out exactly how you want your parser to work, evaluate whether it's fast enough for you or if you need to go to a faster one that will do what you want, if perhaps will more code or more effort.
I'm more interested in doing this using Lisp than anything else. I'm just trying to figure out which Lisp suits my needs the best. Is there one that is particularly suited for this task, or is it just a matter of preference?
In particular, you've said so little about what what exactly you want to parse, what parsers you've tried, and how they haven't suited your needs that I have no way of making further suggestions.
I'm just asking in general for the most part. I have very little planned at the moment.
I've done a little bit of work with parsing, but I'm somewhat new to lisp. And it's a bit difficult to choose between scheme, clojure, common lisp, and arc. The thing that I'll most likely spend most of my time doing with it is parsing and writing toy interpreters, so focusing on the parsing libraries available seemed like a good approach.