I've seen the results of vinyl paint used on a car. It's ok for cars if something needs to be done with it, but like on door panels it will get nicks and scratches from the heavy use.
The PC won't get that heavy use, but if it's plastic and not vinyl, and if the plastic is smooth and not very porous, I'd go with just some reg o'le spray paint. Solvent based, not water born and not lacquer. Arcylic would work well. With the neon green you'll be limited to the type of paint you can find your color in. No problem tho.
With painting it's all about the prep. My suggestion,
Clean foreign matter from the metal and plastic. Use about 320 grit sandpaper and give the plastic a light sanding. Don't leave any spots unsanded. The metal won't need sanded. Clean all the dust and use a dust free area to do the painting. Nothing like having to wait for paint to dry so you can sand out the painted dust, then paint again.
Use the same multi-purpose primer on the metal and the plastic. Just a light coat will do. Doesnt have to be opaque. Just coated. For top coats: inside the chassi a spray can that sprays a dot works better than the ones that spray a fan. For the shell, the fan will work better. After the shell is painted, you could use clear as a finish over the green if you think it needs it. Depends on the product the green comes in. If it's something like the readily aviable florescent green, then I'd recommend a clear coat.
Tip: if you get a run, while it's still wet put a piece of tape on it and pull it off. The resulting mark is easier to deal with than the run...