My dad passed away with dual residency in Georgia and Florida. He had properties in both states. I have to start the process in one state first then to the other. Which state ideally would be the best state to start the process?

First off I don't think there is any such dual residency. It is one or the other. I own property in 2 states and I was told that my will would be presented in the home state and then it is passed on to the non-resident state for settlement. No need for 2 wills, your state of residency is determined by where you file your tax returns.

Catonsville is pretty-much correct. OP needs to determine which state it is in which the dad was domiciled at the time of his death. File a probate petition there. It may be necessary to file a "non-domiciliary ancillary probate administration" in the other state, in order to convey the real estate situated there.

Domicile is where the father last was located with the simultaneous intent that that state be his permanent home. Thus, for example, Alaska is my domicile although I have been in Florida for more than ten years. Where one files tax returns isn't necessarily the deciding factor. In my situation again for example, neither state has income tax. So, in OP's father's case, he may have filed a tax return in Georgia, but that fact wouldn't necessarily decide his domicile.

You need to determine which was his state of domicile - that is, which was his primary residence? You can't have two primary residences, so you need to review his finances to see which he considered his primary residence while the other was considered a second home. In general his domicile is the residence he spent the most time at each year, but it can also depend on such things as which state was his drivers license and car registrations issued by, and where did he vote. I would guess, knowing nothing else, that he may have claimed FL as his domicile in order to avoid paying income tax to GA, but that's just a guess.

Once you have his domicile figured out that determines which state is where you probate the estate. In that state you go through probate for ALL of his assets, including all out-of-state property. Note however that even if the estate is probated in FL, depending on the value of the property in GA there may be a requirement to file and/or pay an estate tax return in GA.

Ancillary administration (in the non-domiciliary state) is general fairly simple. One simply files documents in the court to show that you have been appointed personal representative in decedent's domiciliary state, and asks the court to authorize you to administer the estate's assets in that state (normally by selling the personal and real property or conveying it to the rightful heir(s)). You will also, I believe, have to publish (in the ancillary state) notice to creditors for the requisite period (which may perhaps differ from the period required in the other state).