When and how do I decide to take sellers to arbitration?

First, *why* do you believe that you are legally entitled to payment? If it's simply because these systems are failing or that the sellers performed inadequate maintenance, you are wrong: those things, by themselves, do not entitle you to anything. For the sellers to owe you something for these issues, you need one of the following things to apply:
1) They gave you some sort of written home warranty or guaranty as part of the sale--if they did, you can sue them for breach of contract to enforce the terms of that agreement, if they will not voluntarily pay.
2) The seller knowingly (that is, on purpose; while knowing better) misrepresented (or lied) to you about the condition or shape of the A/C and/or furnace; if they did lie, that would be fraud, and you could sue them based on fraud for compensation (e.g. the repair costs).
But if they did not lie and did not give you a warranty/guaranty, they do not owe you anything; only an agreement to pay for certain costs or active wrongdoing (e.g. fraud) on the part of the seller would obligate them to pay. In the absence of one of the above, this is simply one of the unfortunate costs of homeownership.
(I sympathize: within 4 months of buying a new home, we had to redo two bathrooms because the fixtures did not work right and were coming off the walls. However, the sellers did not lie about the shape of the bathrooms: it was an elderly couple who only lived there part time and whose children had long ago moved out, and they simply had no idea how bad two of their bathrooms were. Therefore, we had no recourse against them.)
If there was a guaranty or fraud, you would, as stated sue the sellers: where to sue (e.g. small claims court) depends on how much money is at stake.