In my experience a machine is far superior to working by hand. If you think you're "interested" in being able to fix your current problem and continue to have one of the best looking cars around on an ongoing basis then spend the time to figure things out and invest in some equipment. A lot less user skill is required to use a random orbital compared to a rotary. You have to really screw things up badly (grit on the pads, completely inappropriate compound choice etc...) to make things worse with a random orbital.
As already mentioned, join a detailing-heavy forum like autotopia, read all of their stickies, FAQs and HOWTOs, ask some questions, and go shopping.
It's worth mentioning that you can reduce the appearance of imperfections in two ways - you can polish the imperfection out (either by completely leveling the surface or by dulling the edges of the micro-scratches so that they don't catch the sunlight any more) or by filling them with a glaze. A pro-detailer also told me that, technically, you can get some improvement too by causing the clearcoat to reshape itself a bit but that's likely only going to happen with a rotary, specific compounds, pads and lots of experience (if it would happen at all).
Although a complete leveling solves your problem permanently (the scratches are completely gone) you've removed material from your entire finish to do so. There's only so much paint and clear coat applied at the factory and clearcoat thickness determines durability and "depth of shine" depending on the finish. "Filling" with a glaze isn't permanent and to some degree the defects are still there. If you aren't careful with your carwash technique and soap choice and/or you don't keep a coat of wax/sealant on top of the glaze you can see your problems slowly come back.
Usually there's a happy medium which comes out with your paint looking flawless but some maintenance and upkeep is required. This is my situation. I do a once-per-year detailing afternoon with clay (if required - often not), multiple compounds applied by ROB as required and two coats of wax. I then target a quick single coat of wax every 4-8 weeks until just before winter (Oct/Nov) when I apply a double coat. If there's a warm sunny day that I can handwash the car and apply a quick coat of wax in Feb I will do so. Often my defects aren't even visible a whole year later. This year they are because the weather didn't allow me to wax since Nov so the layer of protection for the glazes broke down.
Most of the time if it's clean, it's flawless in appearance (except for stone chips). The direct sun cannot catch a single swirl on the surface and it really only takes me one afternoon per year with quick 20min wax jobs every 1-2 months in good weather.
Also be warned that usually in the detailing biz they will use compounds specifically designed to be "easy" and "quick" to hide imperfections with a minimum of work from the detailer using a high speed rotary. Often your problems will be back in just a couple of months because the durability isn't there and the average "detailer" did nothing to actually fix your problem. That is what a typical $100 "detailing" is going to do for you and you'll be back a couple of times per year. This is their business plan. A real fix will cost much more if you pay someone else to do it.
