Ohh where to begin. First, do not use dish soap, it oxidizes paint. There are many soaps made specifically for cars which won't oxidize your paint and will not strip it of any wax thats there. Personally I use almost primarily Meguiars products. They've been around for like 100 years so I figure by now they must have gotten their products right. There is a big section on their web site on how it's all done. You should be able to find a plethora of products at a local automotive supply store.
Thinking along the lines of stuff you can probably easily obtain I would say try meguiars gold class car shampoo and conditioner (soap) for washing. I like the absorber synthetic chamis because they are very gentle on pain for drying. They also make a safe for all wheels wheel cleaner. Since the Insight wheels are clear coated the heavy duty stuff would probably be ok, but it will oxidize the alluminum brake components behind the wheels.
From here it depends how in to it you want to get. Every other month or so my car goes in to the garage and gets a 4 hour clay barring, hand polish and wax. Takes a while, but man does it look nice when done properly. If you want easy a cleaner wax is probably good.
For the interior meguiars professional #40 vinyl and rubber cleane and conditioner is awsome. Apply it to the dash and other tripm pieces and not only does it look good but it smells nice too. Windex will work ok for windows if nothing else, but at costco in the cleaning asile there are some blue cans of glass cleaner which works really well. It can be used safely on plastic too.
For cloths either 100 cotton terry cloth towels or micro fiber towels are the recommendation. There are some diaper type towels that they well that are supposed to be good, but in my experience they trap dirt particles in them and leave them there to scratch your paint as you use it. The nap on a terry towel lifts the dirt away from the paint.
One important thing is to try to keep dirt away from the paint. If you drop your wash mit just throw it away and get another one. Always use clean towels and clean whatever touches the paint. Dust can get trapped in there and ground in to the clear coat causing swirl marks. Though they are really difficult to eliminate all together they can be reduced.
This all comes from my 3 years of driving and detailing cars. I've detailed several perfect vintage cars (are 70's cars vintage?) that have gone through classic car auctions and those several hours of work pay off when the car rolls up on the auction block under all the hot lights and just glistens.
The best is when a car has leather though. Lexol is awsome for leather. It will make is feel and smell better than brand new, even if it's been neglected in the past.
If you can find them here are a few other recommendations on products I have, though find a local distributer may be difficult
Meguiars Detailer Water based dressing
Meguiars Detailer Final detail
" " mild clay bar
Meguiars mirror glaze professional hand polish
So far I've been using meguiars 26 hi tech yellow carnuba wax, but I have this sneaking feeling there is something better. Not sure why, but the stuff does stay pretty strongly for about 2 months
Good luck