For me, the best way to get a clean engine bay is to start with one and keep it that way with constant cleaning. Never let anything build up. Get a leak, fix it.
Everytime I clean the exterior, I clean the engine bay. I bleed everytime I do this trying to get into all the nooks. I prefer old rags that I can toss when done. Sponges tend to hang up too much and be too thick. Take you time and go at it. Detail brushes and a tooth brush will help you in the small places where dirt starts to build. Watch filling up your disti with water. You can use a leaf blower to speed up the drying process and get the standing water out of the nooks and depressions.
Only time I'll use Gunk is when I am looking at a mess. Not great for your wires and hoses IMO. You can try something like Simple Green if you want less toxic. Any solvent runs the risk of removing paint or clearcoat.
Some of what looks like bare metal will have a clearcoat, zinc oxide coating, or is anodized. Once you damage the coating, you are stuck with polishing or refinishing. There are kits you can buy to redo the zinc oxide coating if interested and you get to play with electricity.
Removing undercoating from under the hood is a bear at best. I'm about to try Stoners Bug & Tar Remover. Will report back after I've tried it. I experimented with gasoline on a small section followed by immediate washing and waxing of the spot. Its held up well. As you can expect, working with gas is dangerous to your health and to your paint.
Strongly suggest you wear Nitrile gloves to protect your skin from the nasty chemicals that like to soak through your skin and attack your liver. Latex gloves will NOT protect you from most chemicals you will use on your car.
Wendol makes some good polishes. A Dremel tool helps for the tight places. For larger areas, use a drill. Better yet, you can make a polisher/grinder from an old washing machine motor and a flexible line for your bits. Harbor Freight is your friend. You can use this to port & polish your heads. Just the thing all newbies should try on their own. LOL!
I use Mothers Back to Black on a problem area of my bumpers. I am not pleased with the outcome. I have not tried it under the hood. I'm hunting for a different solution that includes a full repaint to get rid of the black for good.
I do use CD-2 Engine Detailing spray after I have finished cleaning the engine bay. You can spray everything. On very humid days, you need to wipe it down. On dry, it will dry itself very well with minimal wiping. It causes evrything to look wet clean. It evens out the colors of plastic and hoses. It also does wonders for the metals bits. Look at the attached photos. See the shine and even look to the color. These were taken at a show. This stuff can make the difference between first and second place a the shows I attend.
Always have a few rattle cans around so you can do touch-ups of painted parts. Remember this is a high-temp area when you buy paint. Also make sure you go for the right gloss that will match whatever else you have under there. I usually always have black in flat, semi-gloss and gloss.