For out ALU, we started by all the gates we might have to use, to determine which ones were more or less expensive, and how we could make our ALU as cheap as possible. For this we calculated the cost of each gate in 5 different areas which are, from most to least important:
Size, Redstone Powder Used, Redstone Torches Used, Blocks Used, and Repeaters Used
We chose this order because of different reasons: First, we are building this in Creative Mode, meaning we have infinite materials, so the most important thing for us is how small can we make this ALU. Then we decided which materials had more importance, first by how many gates used them (for example the repeater is only used by the Clock, so it isnt very useful for analysis) and then by actual cost/importance of the material in game.
Below we have photos of all our gates (even multiple versions in some cases) and they cost analysis, with a table with all these numbers below that.
Here you can see a full table of all our gates and their values for all the characteristics we chose. For the gates that have 2 versions, we highlighted the worse on in red, meaning we will never use that one. Besides tha you can see that AND and OR are extremely efficient against other gates, with the only one that is better being NOT. You can also see how inefficient XOR is, even though we picked the most compact solution possible for this gate.