Hello, I'm looking to buy some all grain equipment by don't know where to start. If I want to make 10 gallon batches, how big do my kettle, mash tun, etc need to be? Also, do those pieces need to be the same size? I guess I'm not understanding the disconnect in size between the two. Also, what is the advantage of a conical fermenter? Thank you!
Lets see here are my opinion answers to your questions.
Kettle size - I find that it is best to go 5 gallons above what your preboil volumes will be for preventing boilovers due to hot break, etc. (I can make a 15 gallon pot work with a 10 gallon batch, but feel far better with a bigger boil pot.
Tun size - I have a 10 Gallon igloo cooler that I converted with a bazooka screen. I wish they made them a little bigger so may eventually switch to a rectangle cooler or a jacketed pot or something similar. On big beers it can be tight.
One of my mistakes/thoughts when I went to AG was that I forgot about what I was going to do with my sparge water (I batch sparge) while I am draining my first runnings. I use my old 15 gallon pot as a HLT now, but before was using my old starter pot(s) to hold the hot water.
You do not necessarily need everything to be the same size. Since your strike/sparge water dont come to a boil you do not need to worry about boilovers there and can go with a smaller HLT as a result. I am not 100% on the Tun size but depending on the size of your brews, 10 gallons will work, but with a lot of grain, 12 - 15 may be better. It never hurts to have the most space in your boil kettle, though with larger pots, having a welded/weldless port is really nice for draining. Wort gets heavy.
Conicals are the style of fermenter used by big breweries. The nicest thing about them is that you can dump the trub/yeast/what have you from under the beer, and take samples without opening your fermenter. The yeast can then be washed, or tossed or whatever you want to do with them. There is also the oxygen permeablility and sanitation aspects too. Most conicals are stainless which do not scratch as easily as plastic so are easy to clean, plus metal really does not transfer O2 at all. Check out this BYO article for a decent overview of conicals.
https://byo.com/stories/item/524-cylindroconical-fermenters-advanced-brewing