Normally I would suggest an extract kit.
But, 9 days ago I brewed a stove top batch of all grain, with only a 3 gallon pot, a sieve as shown (perhaps a bit bigger than this one), and grains, hops, a packet of windsor dry yeast, 5 oz dextrose.
I filled my pot up nearly to top, got it up to 155, turned heat way down, filled the sieve up to the brim with crushed barley malt, a few oz of specialty grains, and mashed for an 90 mins. My sieve had hooks to set it on top of the pot so it would just span the top of it and not fall in.
I stuck a temp gauge in the malt, and checked it periodically either slightly turning up heat or turning heat off. During this I also placed the cover on as best as I could. I would also dip the sieve completely under the water, and lift up, the grains stayed in quite well. I did this probably 6-7 times for a few minutes each time.
At the end of mashing, simply lifted up the sieve pressed out the remaining liquid, and into the garden it went. Boiled for 60 mins, with three additions of .25oz of willamette, cold water bath, and pitched yeast, didn't expect alot, but had an idea it would be pretty tasty judging from the smell. Mainly did it to try the windsor strain, and also build a yeast cake.
After a few days of fermenting, placed 3 gallon carboy out side for a few night to cold crash it with a garbage can over the top of it to keep light out, also just put a sandwich baggie over the top of it and tied it on around the neck of carboy with a string.
Anyway, I wish I had done something like this in the first place earlier in my brewing trajectory. This beer was Great! Ended up with approximately 2.5 gallons all said and done. Real tasty, force carbed it using the carborator cap. Didn't taste green (young) at all, cold crashing it to below freezing really dropped everything out.
Next time I am going to do this and add some honey to make a small batch of braggot.
So, I don't know if this helps you, but it might give you some ideas on how to get your feet wet...