I refined the concentrations and times for the chemistry. This is not set in stone and you can and should experiment with it but it will give you great results with the tapwater and developer I am using.
Let's get startet ...
You need ..
One scale wich works in the area of 0.0 or 0.00 grams. I have the latter for 10 bucks which works just fine. One spatula. This is really helpful with the very small amount of potassium permanganate you will need.
The chemicals mentioned below. Most of them are from pool maintenance and should be easy to get.
They are also quite cheap.
You do not have to make a one Liter solution! Just make the amounts you need.
You should always wear gloves and glasses (googles) when handling chemicals no matter how dangerous they are. Also: Eating in the darkroom is strictly forbidden !!
I am using Adox Adotol Konstant II a PQ (Phenidone/Hydroquinone) powder developer in stock solution and I am using Adotol Neutrol Eco a concentrate without Hydroquinone usually 1+4. I guess you can use any paper developer you can get your fingers on.
I use round about 200-300 ml solution in a 5x7 tray for my 4x5 prints so I have some space for agitation without splattering around.
I just use plain tapwater. The difference between this and an acid stop bath is 15 seconds in which the print will develop further. Not worth the hassle.
A bath of 30 seconds to 1 minute will suffice.
This bleach is quite harmless but the permanganate makes really bad stains in your clothing and nearly everything it comes in contact with. So work slowly and if you weighing it do not breath into it.
1000 ml water 20 deg. Celsius
25 g NaHSO4 (Sodium metabisulfate)
2 g Potassium Permanganate
You can weigh everything together if you want and give it into the water. Stirr well as this will not solve by its own. You do not want to have any permanganate flakes in this or they will damage the photo by making tiny holes in the surface.
I am using 200 ml of water for my 4x5 prints in a 5x7 tray and it will last for 12 or more prints.
Do not keep this longer than a day, so it is a once only bath.
Agitate all the time and change directions during it. Bleach for round about a minute or at least twice long as it took for the picture to dissappear.
This gets rid of the brownish negative which will be left over from bleaching and it will re-sensitise the paper. You do not really need this but it makes things easier. If you work outside on location in lots of bright light, you probably do not need this. Test what works best for you.
1000 ml water
12.5 g Na2S2O5 (Sodium bisulfite)
I use only 200 ml (2.5 g) here as this stuff is a bit smelly.
DO NOT inhale this directly.
You can reuse it several times. Keep it in an airtight plastic bottle. Agitate for two minutes or at least double the time it took for clearing the paper.
You do not really need one as all silver should be either washed out or developed but it is better to be safe than sorry. I am using Adofix Plus for 1-2 minutes. A fixer can sometimes remove some tints from the print.