If we keep everything as I've shown in the schematic, you'll need at least 2.2A or 2200mA, so a 2500mA supply is good.
Let me clarify a few things then let's look at some alternatives you may want to explore. In the meantime, I strongly suggest not ordering anything until we work out all the kinks - the first few times you tackle an electronics project, there is an almost irresistible temptation to order parts as soon as possible. From first hand experience, don't do it. This will save you a lot of time in the long run as well as money since things can change instantly in the design stage.
Okay, a MOSFET shouldn't run more than a buck or two. Maybe a few bucks on the high side if we need something to handle a lot of current (which we don't), so adding one wouldn't be costly.
Reverse voltage protection applies to the power supply, in this case a DC supply. A DC supply that plugs into a wall will not be affected by how your house is wired. House wiring is AC which does not have a polarity. However, the output plug of DC supply will have a polarity and this is where we concern ourselves. If you study them closely, most supplies use a barrel plug with a tip and a sleeve. You can often get the same size plug in both polarities, i.e., tip positive and sleeve negative OR tip negative and sleeve positive. If someone plugs in a barrel with the wrong polarity, the circuit will be damaged if no protection is on the circuit. Another thing that could happen is the dog chews up the cord and someone decides to fix it but accidentally reverses the polarity.
I agree the bridge rectifier design is nice and allows the circuit to work regardless of polarity or AC or DC is supplied (so long as the voltage is correct).
Alright, your resistor calculations are good (though the webpage shows V_LED is 3.5V), but 0.238W is too close to 0.25W to be safe. Therefore, you'll want to use 0.5W resistors here. But, since you plan to use two digits (front and back), we can get a little clever here. You could wire the 1-inch displays in series, e.g., segment a of the front team A win is wired in series with segment a of the back team A win, which then gives us: 16.6V - 3.7 - 3.7 - 1 = 8.2V. Then R = 410 ohm (470 ohm could be used). This then gets our wattage under 0.18W - while still a little high, this should be okay for 0.25W resistors. You may still want to use 0.5W to be safe. In any case, you also reduce your resistor count to half for the 1-inch displays.
A bridge rectifier can be made with four regular diodes, but since we need over 2A, I suggest we just get a dedicated bridge rectifier. I won't cost much compared to rolling your own and it will be easier to wire since they all have markings on the input and output.
I'm slowly looking through the BOM you sent me for some prototyping supplies. I can help you save several bucks (to a point, depending on shipping from two supplies as opposed to one), but again, I'll need sometime. Take a look at Electronics Express for breadboards and jumper wires or even eBay. But I'll put something together to try to get as much at the best price from the fewest sources as reasonably possible - again, if you have the time to wait.
Let me clarify a few things then let's look at some alternatives you may want to explore. In the meantime, I strongly suggest not ordering anything until we work out all the kinks - the first few times you tackle an electronics project, there is an almost irresistible temptation to order parts as soon as possible. From first hand experience, don't do it. This will save you a lot of time in the long run as well as money since things can change instantly in the design stage.
Okay, a MOSFET shouldn't run more than a buck or two. Maybe a few bucks on the high side if we need something to handle a lot of current (which we don't), so adding one wouldn't be costly.
Reverse voltage protection applies to the power supply, in this case a DC supply. A DC supply that plugs into a wall will not be affected by how your house is wired. House wiring is AC which does not have a polarity. However, the output plug of DC supply will have a polarity and this is where we concern ourselves. If you study them closely, most supplies use a barrel plug with a tip and a sleeve. You can often get the same size plug in both polarities, i.e., tip positive and sleeve negative OR tip negative and sleeve positive. If someone plugs in a barrel with the wrong polarity, the circuit will be damaged if no protection is on the circuit. Another thing that could happen is the dog chews up the cord and someone decides to fix it but accidentally reverses the polarity.
I agree the bridge rectifier design is nice and allows the circuit to work regardless of polarity or AC or DC is supplied (so long as the voltage is correct).
Alright, your resistor calculations are good (though the webpage shows V_LED is 3.5V), but 0.238W is too close to 0.25W to be safe. Therefore, you'll want to use 0.5W resistors here. But, since you plan to use two digits (front and back), we can get a little clever here. You could wire the 1-inch displays in series, e.g., segment a of the front team A win is wired in series with segment a of the back team A win, which then gives us: 16.6V - 3.7 - 3.7 - 1 = 8.2V. Then R = 410 ohm (470 ohm could be used). This then gets our wattage under 0.18W - while still a little high, this should be okay for 0.25W resistors. You may still want to use 0.5W to be safe. In any case, you also reduce your resistor count to half for the 1-inch displays.
A bridge rectifier can be made with four regular diodes, but since we need over 2A, I suggest we just get a dedicated bridge rectifier. I won't cost much compared to rolling your own and it will be easier to wire since they all have markings on the input and output.
I'm slowly looking through the BOM you sent me for some prototyping supplies. I can help you save several bucks (to a point, depending on shipping from two supplies as opposed to one), but again, I'll need sometime. Take a look at Electronics Express for breadboards and jumper wires or even eBay. But I'll put something together to try to get as much at the best price from the fewest sources as reasonably possible - again, if you have the time to wait.