Mechanic work is about the ability to diagnose correctly and accurately. IMO the first thing to do is stop guessing and get to work on the testing to figure out what REALLY went wrong. Assuming you know what’s wrong is a great way to spend lots of time and money fixing all the things that aren’t really the problem.
– Do a combustion gas test (using a test kit with gas-reacting dye) on the radiator to see if you are correct and it really is a blown head gasket. Of course, also check the oil for coolant contamination, smoke, etc if it’s totally obvious, but ultimately it’s the combustion gas test that is the gold standard to see if you have a head gasket leak.
– How’s the compression? Could you have lost a ring instead of a head gasket or is the top end just generally in bad shape? Do a compression test.
– I’d want to know more about that ticking noise and see if I could track it down more precisely. If you go forward with fixing it, I’d want to fix this as well, but again it all starts with knowing what’s wrong.
Then you can build a parts list and start to look at availability and options depending on what you need to do. There may be kits or other options, it all depends on what it needs. Also, depending on what’s wrong, watch YouTube videos to see what you’re getting into and determine if you think it’s within your skillset to do.
I DO NOT like working on ATVs because everything is so shoe-horned in, it’s like working on an ultra-compact car. It seems like Step 1 of every ATV repair is to spend 2 hours taking off plastics, shields, shrouds, harnesses, hoses, the covers to the covers, then the covers themselves, then… It’s a great way to hone your abilities to work in tight spaces, I’ll give it that. This is just my opinion so others will disagree and tell they’re the easiest thing to work on since the Model T, so do your own research.