Drain and Vent size?

Please excuse me if this has already been covered 1 million times. I did some searching and could not come up with an "exact" answer to my particular scenario.

I am adding a 1/2 bath to my home and had some questions on pipe sizes.
The 1/2 bath is also going to double as a laundry room. I am converting a fairly large "mud room" for this that has a crawlspace under it. The room will contain a toilet, pedastal sink, washer/dryer, and a utility sink. This room is directly on the oposite side of my kitchen sink and dishwasher.

Now for the questions:

1. What size supply lines should I be running for all this? I was planning on Teeing off the kitchen supply that is 1/2. Is this acceptable?

2. What size drain should I use to connect to the main? Is 3in enough? Currently I believe there is a 1 1/2in drain for the kitchen sink/dishwasher that I was going to replace.

3. What size vent should I use? 2in??

Thank you in advance for any and all answers.

yes, yes, yes [1,2,3]

yes to all questions. Nothing mission critical here.

david

Thank you for confirming my answers David!

1/2" pipe is too small for all those fixtures on the water supply.

https://terrylove.com/watersize.htm

Toilet can go 3", 2" vent
Kitchen sink should be 2" waste 1.5" trap arm and trap, 1.5" vent
Washer 2" waste, 2" p-trap, 1.5" vent
Utility sink, 2" waste, 1.5" trap and arm, 1.5" vent
Pedestal lav, 1.5" waste, 1.5 trap, 1.5" vent


Washer and utility sink, with 2" standpipe for the washer
Hammer arrestors on the water supply.

Thanks Terry. So should I use 3/4?

How about the drain and vent? Should I still use a 3in drain and 2in vent for all of these considering I put all the traps/drains for each according to the listed sizes? These will all be connecting together to connect to the existing system leaving the house. (this is on the opposite side of the house in the basement)