The Vault Suit is the correct choice.
My first character was still wearing the vault suit at level 20, despite trying a number of alternatives. This is mainly due to the suit's radiation resistance.
Other undergarments are somewhat useful due to bonuses to SPECIAL attributes, but as soon as you run into some radiation you get toasted, whereas that same radiation would have barely registered with the vault suit on. Still, these other undergarments have situational uses. Undergarments that add to CHA can be a huge help when bartering or persuading. Undergarments that add to INT are good to put on before turning in quests.
The BOS Uniform grants 5 rad resist, so that might be a possibility as well. However, you can't upgrade the BOS Uniform. This means that it is quickly outclassed by the vault suit, which can be upgraded multiple times. You could also consider wearing headgear that has rad resists, like an Assault Gas Mask, but then you miss out on the attribute bonuses from a hat and glasses and look like a goon.
Later in the game you can get radiation resistance from your armor. By level 13, you can get Armorer 2 and Science! 1, allowing you to add the Leaded Misc mod to your armor. You can easily get 50 or more rad resist without a Vault Suit at this point. That's enough for almost any situation, so you can switch to different undergarments if you like. One easily obtained alternative is the Minuteman Outfit, which adds to AGI and PER. Preston is wearing one of these, and the clothing stand I built in Sanctuary Hills has two in stock every day.
More details on available clothing here, but that list doesn't look comprehensive at this time.