Evapo-Rust is good for small stuff, particularly small, chrome plated stuff. It will leave a sticky residue if left to dry, but rinses off fine. It is very expensive if you are trying to immersion soak a frame, handlebars, rims, etc. Be very careful with some of the older red paints and Evapo-Rust because it may turn them pink (also true of oxalic acid). If iron oxide pigment is used in the paint because it will leech out he iron oxide component, turn the red to pink. It will also soften/melt some of the older type water-slide decals. I love using it in a little dish on headset parts, bottom bracket parts, brake handles, brake calipers, etc. It also works very well if you want to remove rust from the inside of a set of handlebars (fill the insides and let it sit a couple hours, then pour out into a jar.
I don't use CLR on bikes and parts because Evapo-Rust works as a higher end solution for small stuff and oxalic acid is an effective and economical solution for larger parts and baths.
Your bike will probably clean up pretty well. I don't see anything particularly lethal on the surface, at least from what I can see.