I was just wondering what I would need to remove or add to my 1998 neon highline to put in a DOHC engine. I already have gotten rid of the air intake over the top of the engine (which is why DOHC had the hood "bump") But I am not sure if I need anything else.

The bulge hood is there to clear the second cam in the engine. It sits a little bit higher.

So if I got a DOHC and attempted to put it in my car without the hood bulge, would I experience any overly troublesome problems?

The hood may rub on the cam timing cover. I have seen some drop in with no problem others do rub. You can either buy a bulge hood or just cut out the bracing on the flat hood (SOHC).

So if I decided to go with a DOHC what kind of extra parts and pieces am I looking at modifying or buying to make this thing work?

You need just about everything from the DOHC including the complete engine, wiring harness, PCM and motor mounts.