puma1824- IMO the mindset here should be "realistic improvement". Unless you want to really go nuts (especially in the sense of expense), I'd aim for "clean and much better" and not pursue concours-quality perfection.
I do like some of my "fancy tools" for jobs like this, but I've also brought back engine compartments (and undercarriages...I'd do that too on that car but it's another topic for another thread...) that were worse than that with just the right products and a *LOT* of time.
As noted, clean off all the grime. Note that I'm a big fan of (safe) solvents as it's easy to control what's going on and there's no need for rinsing. Yeah, I use degreasers/Engine Cleaners/APCs/etc., but I still think the solvent approach is worth mentioning (ValuGard's New Car Prep comes to mind) if only for tight spots and areas where you want that good control over the proceedings.
Avoid regular Simple Green as it's toxic to bare aluminum.
Rusty fasteners (bolts/etc.) and fittings- I'd just replace them. For those that you won't/can't replace, try Wurth's Rost-Off instead of silicone-rich penetrating oils such as the otherwise great PB Blaster (which can limit your options later). Sometimes KRC7 (made for bathroom fixtures) can work great on corroded bits that have zinc/etc. finishes (bits with that "white corrosion").
Lightly rusted black metal bits can be rejuvenated surprisingly well with BlackFire's Gloss Enhancing Polish (I know, sounds nutty, but it works very well for me, even on nasty stuff like surface-rusted brake drums. Use multiple applications, top with something durable or at least BF's AFPP).
Worse rusted black metal bits- I use Autoglym's Bumper Care (another wacky approach that works incredibly well). It's also good for underhood plastics that are too far gone for a "trim sealant" approach (which I do prefer if it's feasible). Note that the Bumper Care and Wurth's Rubber Care are *ONLY* "slime approaches" that I use under the hood as other stuff a) doesn't work as well for me in this application and b) is more likely to retain dust/dirt, making future maintenance a chore. I the black plastic isn't too bad, try just cleaning it and then using a leaves-stuff-behind QD on it (I prefer ValuGard's Fast Finish for black plastics). Again, I like this better than the other usual approaches especially with regard to ongoing upkeep.
Also worth a mention- Griot's Rubber Prep, a [freakin'] miracle product IME.
Rusty painted metal- Instead of the popular POR15, I use Rust Bullet or KBS Coatings' Rust Seal or Eastwood's Rust Encapsulator. I'd also want a can of Eastwood's Black Heavy Duty Anti-Rust, an undercoating that penentrates/adheres to rusty metal and dries like a black paint.
