Suppose you completely empty your mind of all thoughts
This is what happens when you go into deep sleep. When you don't dream, the mind falls back to the Bhavanga process. This is called the passive state of the mind. It is what keeps you alive, when there's no other thought. This Bhavanga process is the result of your birth Karma.
Suppose that in that state you make a choice to arise a thought
No, you can't make any choices when you are in Bhavanga state. The Bhavanga process should first be interrupted by one of the sense doors. Volition comes much later in the process.
A complete thought process, occurring through the physical sense doors, is made up of seventeen thought moments (citta kha.na). These are:
- A bhava"nga that flows by in a passive state when one of the five physical sense organs comes in contact with its object (atiita bhava"nga).
- A bhava"nga that vibrates for one thought moment (bhava"nga calana).
- A bhava"nga that cuts off the flow (bhava"nga upaccheda).
- A citta that turns towards the object through the sense door that has been stimulated (pañcadvaara-vajjana).
- The appropriate sense consciousness; in the case of the eye, for example, eye consciousness (cakkhu viññaa.na).
- Next a thought moment — the sampa.ticchana citta — which has the function of receiving the object.
- When the object has been received another thought moment, called the santiirana citta, arises, performing the function of investigating the object.
- The act (kamma) itself, especially if it was a weighty one.
9 to 15. The object having been determined, the most important stage from an ethical standpoint follows. This stage, called javana, consists of seven consecutive thought moments all having an identical nature. It is at this stage that good or evil is done, depending on whether the cittas have wholesome or unwholesome roots. Therefore, these javana thought moments have roots and also produce new kamma.
16 and 17. Following the seventh javana the registering stage occurs, composed of two thought moments called tadaalambane. When the second registering citta has perished, the bhava"nga follows, flowing on until interrupted by another thought process.
As you can see, decision making starts at the 8th stage of the process.
Thus, the first thing that arise is 'mental fermentations/volitions',
which leads to the arising of thoughts.
The first unit of Paticca Samuppada is given as ignorance. But that doesn't mean it started from ignorance. There's no real starting point. It's like asking the starting point of a circle. It's wherever you hold it first. The standard Paticca Samuppada teaching spans over 3 consecutive lives. The past, the present and the future.