Let me lead off with this warning: I don't have enough experience as a vintner to provide a definitive answer, but here are a few thoughts to consider:
*Most kits start with 6 gallons in primary, a portion of which is left behind with the lees each time you rack to another vessel. Thus, you actually need the largest vessel to start, then smaller ones as the process proceeds - many vintners actually start with the bucket, then use 5-gallon glass carboys for secondary & further racking, and supplement with half-gallon or smaller bottles for the excess, using the smaller bottles to top off the carboys as wine is lost to the lees.
*It depends on the yeast somewhat, as to the amount of foam (krausen, for beer brewers) that will be produced, but many of the widely-available Lalvin yeasts are specifically described as "low-foaming" (e.g., Bourgovin RC 212, D-47, EC-1118).
*Is there a grape pack included in the kit? If so, the grapes will displace some of the must when they rehydrate, making a larger volume fermenter necessary.
Good luck!