For a normal person just washing a normal car in the drive way don't over think it. Don't get too overboard or it won't be fun and you won't do it. Here is what I would do.
Get three buckets, one for rinse one for wash one for wheels/tires. On the wash bucket mark the outside with lines of gallon intervals so you know how much soap to add. Don't worry about the grit guards, most here use them, i do in all my buckets but if you don't, your car isn't going to notice.
Real carwash soap, get what is on sale, a jug will last a year or two of washing your own car in the driveway.
Get a wash mit not a sponge
For wheels and tires a wheel cleaner works on both, just a couple squirts on the wheel and tire. You already have a tire and wheel brush so you are good, just know either one isn't for the body.
If you don't have a polisher and have no interest in one just get some quality sealant even Meguiars Ultimate Wax (really a sealant) works great, is easy to use, and produces great results.
Get the corresponding spray wax, after you wash while the car is still wet sqirt a spray or two per panel then dry like normal. With that a couple times a month you should get great longevity on your protection. If you wax in spring and fall you will be great.
That would be what I would do for the outside.
Inside Stoners aerosol glass cleaner works well and is inexpensive.
Find a all in one cleaner protectant like Meguiars quick interior detailer. I use it, but am going to try something different next, the smell isn't the greatest. If you keep up on the interior that should be enough for cleaning.
If you have leather again a cleaner protectant is where I would go. They work, and without too much work.
Yes there are other ways to go, personally I do it a bit different, but spending hours cleaning my car is fun, it gets me out of the house and is my break. If spending 3+ hours every other week isn't in your cards what I suggested will work.
If you want to purchase special towels for drying, special ones for wheels, special ones for tires, special ones... you get the idea again great we can help, but for new people that is overwhelming and expensive. For the average person who just wants a clean car to go to work people used old bath towels for years and never thought different.
Remember you want to keep this fun, it's easy to get so much stuff for every little thing it isn't fun anymore and you won't use any of it.
Another idea is pay a detailer once a year to get your car perfect then just maintain it best you can.