I have more experience with infusions and other ferments. I'm ready to delve into beer making without buying an expensive kit. What's the best way to do this?
This is not a great hobby if your goal is to save money on beer costs. It takes a long time to recoup the cost of equipment when you save pennies per glass. And there is always more equipment to try...
That being said, the cheapest and lowest risk way to get into the hobby with making one-gallon batches. You can get a one-gallon recipe/ingredient kit from Northern Brewer for $12.50, before tax and shipping. Check your local homebrew store (LHBS). Buy a one-gallon container of apple juice at the grocery store that has a recycling symbol 2 on it. Other supplies you will need from the LHBS include a $0.50 grommet for an airlock, a $1.50 airlock, and the smallest bottle of Star-San or Iodophor that they have (should be about $8), and about four feet of PVC tubing ($2). You need a 1.75 gallon spaghetti pot and a large metal stirring spoon from your kitchen. And you will need a kitchen thermometer that can read between 50-80°F at a minimum -- a meat thermometer can work. When you are ready to bottle, you will either need swing-top bottles, or a bottle capper and caps ($15).
Drink the juice. Drill a hole in the lid of the juice big enough to fir the grommet. Watch Northern Brewer's video on one-gallon brewing on youtube, and then brew according to the directions that came in the recipe/ingredient kit.
But it may be cheaper to spend $50 to buy the one-gallon beer making equipment kit from Northern Brewer, which comes with on free recipe/ingredient kit.
The more you do (the less others do for you) and the more you buy the cheaper it will be. Go all-grain, grind your own grain, buy in bulk.
Assuming you can store them properly, begin buying base malts and hops in larger volumes. Since you'll likely have only a few malt varieties on hand, you 'll need to adjust your recipes to use the base malts you have or adjust your brew schedule to make beers that use those malts.
After startup cost of equipment, ingredients can be cheap if you brew within a somewhat narrow style range and buy ingredients in bulk. That said you can almost eliminate startup costs if you choose to brew in smaller batch sizes that allows you to use equipment you already have. Like your largest stock pot and you sink for chilling.
As you get better at the entire brewing process saving and repitching yeast saves on cost as well.
That said it isn't the cheapest hobby as we all tend to keep expanding our efforts.
I always recommend to novice brewers that they try to make a 1 gallon batch before investing in all the equipment. Most people already have kitchen equipment suitable for making 1 gallon of beer and any additional equipment is easy to find like a 1 gallon glass or plastic jug. Any decent homebrew supply shop should sell 1lb bags of malt which you can make a small batch with. You will definitely have hops leftover unless you use the same hop for aroma, flavor, and bittering.