The battle of Alesia always struck me as an odd thing for Vercingetorix to have invited. Prior to the siege, he had committed to several months of guerilla warfare and scorched-earth-and-retreating. Shortly before the battle of Alesia, the Gauls had lost the battle of Avaricum in a similar siege. After that, they won the battle of Gergovia, but instead of trying to continue their guerilla warfare, they retreated to Alesia to try and withstand another siege. Why the sudden shift in tactics? It doesn't seem like putting a giant amount of Gauls in Alesia was a great idea. It also doesn't seem like Vercingetorix's plan was to try and force the Romans into a decisive battle on two fronts either. It ended up that way, but only because some of Vercingetorix's riders were able to escape and call for help.
Vercingetorix's coalition was not only a military process, but was set into an important political context as well : not only due to the strategic goal of removing Romans out of Gaul, but also in its building-up and making-up.
Gaulish military coalitions involved different polities or factions each with their own interests and objectives : being united against Rome to recover their political freedom was a thing, but not everyone had the same idea of how or why doing so. Vercingetorix's war council (concilium armatum) was thus not a general staff as Caesar benefited, an ensemble of subordinated officers assisting in applying strategic and tacts, but a council that he had to arbitle and negotiate with (although in a position of strength). This is not exclusive to the Gaulish conception of warfare, of course : among other exemples, the Persian war or the campaigns of Pompey against Caesar illustrate that ancient military commanders often had to deal with their allies, their state(s) or even their own clientele.
But, on the other hand, the formality of such a coalition in ancient Gaul necessarily implied that it had to be the political, even legal, basis of Vercingetorix's summa imperii and, with the assembly held at Bibracte, his imperium. You'll find a somehow more complete description of this military imperium in Gaul there (in the third sub-post), but it's worth looking at the make-up of a coalition.
Vercingetorix actually had to go over that twice, first in the winter of 53/52 BCE where already armed and prepared, he took the lead of a rebellion against Romans (that Indutiomaros went close to do in 54 BCE) largely involving western Gaulish peoples on his own person, secondly after the success of Gergovia in a more formal and "legal" way by convening the Assembly of All-Gaul and receiving a formal imperium but also principatus, both for him and the Arverni as chief people. While it definitely allowed a legalization and the further growth of his rebellion, it also complexified its management on military and political grounds : in discussing Vercingetorix's strategic choices, this is a necessary context.
With that in mind, what was this strategy, or rather, what were his strategies?
The idea that Romans had to be expelled out of Gaul wasn't proper to the young warchief, motivating the Belgian revolts in 54 and 53 BCE (which involved Celtic peoples as well) : while the death of Indutiomaros and Acco prevented the make-up of a formal coalition.in these events, the immediate strategy of Vercingetorix, once his coup in the Arvern petty-state successful, was to gather the means building one and endorsing the expected role of a commander-in-chief in spite of a debatable legitimacy.
It’s not clear how much Vercingetorix was involved with the planned uprising and the slaughter of Roman traders at Cenabum, led and decided by Cotuatos and Conconnetodumnos; either factions leaders or chief magistrates of the Carnutes along their gutuater (possibly a “senior druid”), but the newly proclaimed Arvern king soon took the head of the general revolt in Gaul : that meant sending envoys and displaying his military capacities beyond gathering a force made of clients and mercenaries.
Having obtained the approbation of the peoples of western Gaul as well, seemingly, the Arverni clients and organized a first war council and decentralized command, his first strategy was to pressure both Gaulish peoples that did not join his coalition and Romans in a series of movement tactics : sending troops to force the allegiance of Bituriges from the Aedun sphere of influence (and, later, seemingly threatening to do the same with the Boii moving to their oppidum of Gorgobina), but as well moving Lucterios to the edge of the Roman province of Gaul searching, inconclusively, to move peoples under Roman domination to his side, display political and military commitment, and eventually to force Caesar to react.