I have used this checklist every year and have had no problems:
https://www.catalina36.org/members/technical/maintenance/rich-lemieuxs-d...

Rich has a very thoughtful list.

I'll add a couple things that may be relevant. If you have an anchor wash down pump I would just disconnect the hoses and let it gravity drain. I say this because antifreeze exposure has crazed/cracked the bowl on my surflow raw water strainer that feeds the pump. It's done this twice and a replacement unit is not cheap. The clear bowls used in all the other filtration areas of our boat have been fine with antifreeze exposure, but not the surflow unit.

If you have AC, I would suggest disconnecting the water inlet/outlet hoses and blowing out the copper coils with air. I use the pump for our inflatable for this and do the same with our water heater rather use antifreeze.

Welcome! We too moved up from a C30.

Welcome to the forum!  You will find a lot of helpful people and posts here.  Where you keep the boat and whether she's in water or on the hard can make a difference as well.  

Hello.  I am a relatively new Catalina 36 owner.  She is named Trilogy.  She is a Mark 1 with Hull #0053.  Her home port is Pass Christian, Mississippi- on the Gulf coast.  Thank you to everyone who has posted their hard-learned lessons here for all of us to learn from.  If I have some sage advice to pass along, I will.  

Skip

Welcome to the forum and congrats on your new boat!
JEB

Skip, as most have done, please put your boat/home port info at sign off spot. It is helpful for us to respond with info that may be applicable to your boat.  Once you set it up, it loads automatically.