I am sorry to ask such obvious questions,however,my grandpa always told me that the only dumb question was the one that wasnt asked. What is better for cheddar,waxing or patching with muslin?

Your Grandpa was almost right.  I have, actually, heard some pretty dumb questions.  Yours, however, is not in that category.  It’s a matter of personal preference.  Wax is kind of traditional, but I’ve had trouble in the past with cracking.  If the wax cracks, mold can form under the wax and ruin at least part of your cheese.  It requires regular inspections and remediation as necessary.  Bandaging, or patching as you called it, is even more traditional.  This is how cheese was aged before wax came available.  It, too, requires regular inspections, and additional applications of lard, or whatever grease you use to coat the bandage.  And a rather thick layer of mold will develop on the surface, which is ugly, but should come off with the bandage when you open the wheel.  A third option, and the one that I have personally gone to, is vacuum sealing.  I have had less difficulty with this method than with the other two, but occasionally a seal goes bad and it must be opened and re-sealed. 

So, each system has it’s drawbacks, and it’s really up to you as to what fits your personality and lifestyle the best.

Another decision you’ll face is this:  how long will you age your cheese?  If you use raw milk, which is the best, you will need to age for a minimum of 60 days.  But with cheddar, you’ll want to age longer than that to get a fuller flavor.  Probably 4 months would be good for a mild cheddar, 6 months for medium, and longer for sharp.  Some have aged for as long as 2 years - but their patience exceeds mine.

So, onward and upward!

OK, but how does the cheese “breath” in a vacuum seal? I am embarrased that I am this naive on the process. I better start a little less gung-ho.

This is just my opinion, and I’m not a cheese scholar:  In my opinion, there’s not a whole lot of breathing going on.  The wax and greased bandage cannot allow for much, if any air passage.  There is likely just as much air left in a vacuum pack as there would be under the coating of wax.  If there were any significant amount of air passage, it would result in even more drying of the cheese, and we don’t see that.

And here’s another advantage to vacuum sealing:  It is not necessary for the surface to completely dry prior to sealing, as it would need to be with waxing.  Therefore, there is no rind on the finished wheel.

As I see it, it’s a matter of personal preference.

You could try gauzz and wax, that way the wax will not crack, also make sure its not thin, that will create allot of problems.
Best thing is to try them your self and see what you like. I always use wax and do a nice thick layer.

I always thought the wax looked nice,however,I need to concentrate on quality I suppose. The adventure is where you end up with the wisdom of how you got there.

I’m not so sure gauze would prevent cracks.  It might just hold them together better.  But since I’ve not done it that way, I can’t be authoritative on the subject.  Actually, one of the major reasons for my preferring vac sealing is that wax is so messy to work with.