Yes, you'll need a burner, but they are part of what you might buy w/ the extra money saved by buying the kit. A turkey-fryer burner can work for that if it produces enough BTUs. I have one that produces 54,000 btus and it's fine. You can find propane burners for in the area of $35, or if someone already has a turkey fryer burner, lots of people use those for brewing.
BTW, I remember very clearly what it is like to be new at this brewing thing. There's all this new terminology that doesn't click (sparge, hydrometer, mash tun, specific gravity, etc. etc. etc), and you're trying to get equipiment that will work well without breaking the bank. And if you're like me, you know you're going to make a few choices you'll wish you had back.
Our feedback for you is in hopes you can have fewer of those choices you will wish you had back. In other words, what are you going to wish you'd done 3 months from now?
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What makes the more expensive kit better (and it is, a lot better)?
One concern is fermenter size. The cheaper kit has a 6-gallon size, the other a 7-gallon size. If you get a lot of krausen--the foam on top of the beer as it's fermenting--you may exceed the capacity of the fermenter to contain it. You rarely if ever will with a 7-gallon size. I have a different brand, 6.5-gallon size, and while I've been close, I haven't exceeded it. With a 6-gallon fermenter, I'd have had a blowout through the airlock.
Second concern is kettle size. This really is important. Yes, there are ways around small kettle size with extract and other kits, but they aren't optimal. The more expensive kit includes an 8.5-gallon kettle. It will be very difficult to have a boilover w/ the larger kettle. As you progress with this--and I'll bet you $10 you get hooked on brewing--you'll want to do 5-gallon batches.
Five-gallon batches are the standard homebrewing batch size. Since there are four of you, trust me--and really, trust me here--you're not going to want small batches. You WILL want the larger kettle within a month or two. As you progress, you'll begin to brew recipes you find, and the vast majority are for 5-gallon batches.
Further, that larger kettle has a ball valve on it, which the smaller 5-gallon kettle does not. It also has a second port into which you could later, if you wanted, install a thermometer that reads directly what the temperature of the kettle is.
Third concern, you want that immersion chiller. You have to cool down the beer before you pitch the yeast; if it's too warm you'll kill the yeast. Chilling quickly also promotes "cold break" which is a precipitation of proteins out of the wort that you have just boiled.
The kettle is a huge upgrade over the dime-a-dozen 5-gallon kettle in the cheaper kit. You want the 7-gallon fermenter instead of the 6-gallon fermenter. And you really will want the chiller. It can take over an hour to chill using an ice bath, and far longer if you just let it sit. Unless you want your brew days to be long, long, long, you want a chiller.
This is worth well more than the $100 difference--and you don't have to screw around with making a bunch of decisions.
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I started out w/ a kit--but I had to buy a hydrometer, there was no spoon, it didn't come w/ any Star-San sanitizer.....and this is the kind of stuff that, as a newbie, I didn't necessarily know I needed. If I were starting again, no question--this is the kit I'd get. And it would have saved me a ton of money.
The morebeer Premium kit is a remarkable collection of items you need for brewing. You'll still have about $90 left after the $230 cost to buy a burner if needed, and maybe some bottles and extra caps. If someone has a propane grill with a propane tank, you're set there as long as you have enough gas.
Linda, in the 15 months since I started, I've brewed 24 batches. The first three were extract batches (which is where you should start to learn the process), then I went to all-grain. I started kegging my beer, built a keezer so I have tap beer on hand all the time at home, bought a Reverse-Osmosis filter system to provide me with brewing water (my tap water is NG for brewing most beers), and I've made some really good beer.
I just upgraded to a bigger 10-gallon Spike Brewing kettle, since my 8-gallon wouldn't accommodate the new Jaded Hydra chiller I bought), and bought a new Blichmann Hellfire burner. BTW, I have a friend who's getting into brewing, he's now the proud owner of my former kettle and immersion chiller. Sucked him right into this, did I.
But he's having fun and loved the first beer (an IPA that Yooper has a recipe for here on HBT), and he is antsy to do it again.
In other words, I've come a long way since November 2015. I remember what it is like to be new. I remember trying to make all the equipment decisions. The Morebeer Premium kit is it. Look no further. Buy it and brew the kit they include.
Just do it, Linda!
<my 2 cents. YMMV. Void where prohibited by law.>