Normally we oversubscribe panels quite a lot because the chance is remote that all circuits will be fully loaded at the same time. However when a single load is 60A and definitely will run continuously when it runs, that only leaves 40A for all the other circuits to share. That's a little bit small for that "oversubscribe" logic to really work.
You might consider making the subpanel 125, 150 or even 200A. There is nothing wrong with a subpanel being the same current as the main panel.
Since the subpanel is right next to the main panel, you don't need a main breaker in the subpanel. However if a subpanel does have a main breaker, its only purpose is a shutoff switch, so its breaker size doesn't matter (as long as it's not too small.) You might consider using a panel with a 200A main breaker, as a hedge against some future when you move all the circuits to that panel, and switch it over to become your main panel.
For that matter, with power company and inspector approval, you can lay it alongside and make both of them main panels under the tap rules. (this is how it's handled when an all-electric house has 400A service; they fit two 200A main panels).
Now back to your original question, about wire sizes, firstoff, the 6 AWG is out of the question, and I wouldn't use copper wires anyway for big stuff like this. I'd use aluminum. Really. The lugs on the panels will all be aluminum, and copper wires on aluminum lugs means dissimilar metals, differing expansion rates, galvanic corrosion, i.e. all the stuff that makes small aluminum wire scary. Aluminum is also 1/3 the cost and half the weight for the same ampacity.
Anyway, once you have decided your metal and ampacity, it's off to see the wizard to get the wire sizes. Put in 240V and 3% loss.** The wizard says for 100A, #1 Copper, or 1/0 Aluminum.
Obviously five feet of it won't cost much either way, but I would still favor Al because of the metal-compatibility issue with your lugs.
**Just to be clear, when you are doing long runs, also try it with 30% loss. That will force the tool to fall back on the minimum permitted size (irrespective of length), and will tell you what actual voltage drop you'd have if you used that. Often it'll be like 3.7% and you may decide 0.7% isn't worth spending $400 more on wire. Or you can play "what-if" until you strike a balance between cost and voltage drop. Won't be an issue in this case.
Well, you asked several questions and if you search on this site you will find many questions and answers regarding sub-panels. We have covered this same subject many times. It may be the most asked questions from novices.
It would be a Code violation, and safety issue, to protect #6 wire with a 100 amp breaker. You will need #3 copper or #1 aluminum if you want to protect it with a 100 amp breaker. You can use whatever size panel you want at the garage but if you want to fully utilize it you should feed it with proper sized wire and protect that with a properly sized breaker.
You can drive the ground rod with a fence post driver they sell at the farm centers. If you have good soil they are easy to drive.
The #6 grounding electrode conductor connects to the ground bus and the neutral bus is kept isolated. Take the green screw (or the jumper strap) that came with your panel and throw it away.
Good luck and stay safe!
Best Answer
Go big, Big, BIG on the subpanel
Especially if your main panel is getting full, and having double-stuff breakers in it definitely counts as "getting full".
We have so many questions on here of "My panel is full. What can I do?" And our answers are expensive and regretful. But that we could go back in time, to when that panel was being bought, and say "Spend a couple lattes on a bigger panel". So, we say it now. Go big. Really big.
You're at 7 breakers so far (2 for the heater) + a foreseeable dust collector and EVSE, so 10. I like to finish with all full-size breakers and >50% of spaces unused, so a 20-24 space panel. Disregard "x circuits" as that calls for double-stuff breakers which are no longer viable due to Code changes. (they don't mention that in the marketing materials :b)
Don't let panel bus rating hold you back: An "R" rated tire is only rated for 85 mph, would you put that on your car? Not willingly! So it's not a win to get a panel with 100A busing. So don't think twice about a main-lug breaker that's 225A/24 space if you can find a happy price on it.
The main breaker doesn't buy you anything (sometimes main-breaker panels come bundled with some bonus breakers, so that can be a savings), but the main breaker per se is irrelevant. You can't make the more convenient breaker trip first, because of main vs branch trip curves and Murphy's Law. Even if you needed a main disconnect switch, the trip value is irrelevant; feel free to feed a 225A subpanel from a 30A feed breaker. Totally legit.
Your feeder wire
2/2/2/4 is an unnecessary size, but I understand why it seems correct.
First, if it's convenient to run conduit from the main to subpanel, and you want to do that, use THHN/THWN-2 individual wires inside the conduit.
Don't bother with copper unless it's like a 10 foot run or something. The lugs the subpanel will be aluminum anyway because aluminum lugs play nicely with both. So why create a dissimilar metal "problem"? (isn't actually much of a problem on these fat feeders). But if you do go copper, #3 will suffice and #8 Cu ground is all you need.
If you go aluminum (most of us would), you need #1 AWG.
Loads
You're in very good shape. Your PC and tools will chomp only 15A of your 100A. Electric garage heaters range from 15A to 50A, but you're definitely covered, even with a 60A sub. But stay at 100A.
Here's why I don't think 100A in a garage is overkill. The automotive world is changing so very fast. "Range anxiety" which used to stop the electric car industry dead in its tracks, is being alleviated from both ends: First, consumers are becoming much more aware of their actual driving patterns. And second, Tesla and others are making is making enroute recharging look stupid-easy. I do lots of transcon trips, and Tesla is at the point where I could recharge in the time I already stop for gas, bathroom, and meals. So EVs are happening, so having 50-80A of headroom in a garage panel is great, and can only help resale value.