I bought the same starter kit from my local store and it worked great. I brewed a pale ale from a kit with dry yeast and it turned out great.
When I went to brew my second batch I bought / made the following items:
- Long clip on thermometer to keep an eye on the temp for steeping grains as well as check the temp during the wort cool down
- Second liquid thermometer for my glass carboy to monitor the temp during my secondary
- Built a wort chiller from flexible cooper, tubing and a funnel (I couldn't figure out how else to attach it to my kitchen faucet)
- Also don't forget ice - I stick my pot in an ice bath and run my wort chiller through it and I can get my wort cooled in about 10 mins
This website helped me out a ton before I brewed my first batch. It's good overview basic videos.
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