Given your background, I think what you're asking is mainly question 1. Here's a few answers to Why Lisp? I use Lisp because it's closer to the way I think. It allows me not to have to worry about variable types. [0] It has integers that aren't bounded. [1] There's a REPL. [2]
Now, given Lisp, why Arc? I like Arc because, although I haven't tried out a lot of Lisps (I'm only on chapter 7 of ANSI Common Lisp, so I'm just learning), it seems concise. I like that it's evolving, and I like pg's goal of trying to make shorter programs. I don't like how long keywords are in many Lisps. Arc is a good Lisp getting better.
[0]You can assign types to variables in Lisp, but this only needs to be done for speed.
[1]My friend and I talk about Project Euler often. He's using C; I'm using Arc. I've never had to worry about integer overflow. He's had to use a 200-cell array of integers to simulate a 200-digit number, and he's had to write his own operators to add, subtract, multiply, and divide these arrays.
[2]Read Evaluate Print Loop. If you use Bash, or the Windows command shell, imagine having to open up a text editor, type in your command, save it, and run it to do any command. This is what compiling feels like to me now.
