Products that require a "machine" to work are typically designed to remedy a problem such as swirl marks, paint contamination, light scratches, etc. You really do not need a machine of any sort for normal maintenance care of your paint.
I'd recommend that you first invest in two 5-gallon buckets, one for your soap and water solution and the other for rinse water. Then invest in a good wash mitt or chenille sponge for the paint and a regular synthetic sponge for your wheels, step bars and other items that catch a lot of dirt but aren't painted or "appearance" items.
The synthetic wheel sponge should never see the bucket of soap solution for the paint. Keep them apart. I use a sprayer bottle full of Meguiar's All Purpose Cleaner (APC) diluted 4:1 for my wheels and step bars. When I clean those items, I wet them, spray them down with the APC and then scrub them clean with the sponge. That sponge then gets rinsed out and put away before I start on the painted areas.
For the painted areas I use the two buckets as such: Soak the chenille sponge or mitt in the soap solution and then wash the vehicle working from the top-most areas, down to the lower most areas. Before I re-soak the sponge in the soap solution, I dunk it in the rinse bucket and wring it out. Then I soak it again in the soap solution. In this way I make sure that most of the dirt and grime that the chenille sponge or mitt has removed from the paint has been rinsed out in the rinse bucket. This keeps the soap solution "cleaner" longer and keeps you from putting grime back onto the paint with each new dose of soap.
Typically I will wash a large body panel (hood, roof, door, fender, etc.) and then immediately rinse it off with the hose before moving on to the next. This keeps the soap from drying on the paint. Periodically I will go back and spray down the areas I've already rinsed just to keep the water from drying and leaving hard water spots. If your area doesn't have hard water, you can probably omit that.
Once the vehicle is washed, I'll remove the hose nozzle and just run water straight from the hose across the vehicle, from top to bottom. The normal sheeting action of water removes the bulk of the droplets that were there from washing and rinsing, and makes drying the vehicle far easier and faster.
For drying I'll use an Absorber synthetic chamois cloth.
Lastly, every other wash or so I'll apply some Meguiar's NXT wax to the vehicle. Thin coats do the job.
Hope this helps.