Your deck can include any version of a character you like, and can in fact include multiple versions if you like, which you can swap out with each other. From Rules Compendium 1.9.2 page 6:
As a Noon play, you can replace your dude card in play with a different version of that dude from your hand. The new card replaces the old, keeping all goods, spells, tokens, and markers, and remains under any game effects. The card that was replaced goes to your discard pile.
However, you can only replace a dude card with another dude card whose experience level is no more than one greater or lower (non-experienced dudes are considered experience level 0). Thus you can replace a non-experienced dude with the Experienced 1 version, and vice versa. You can replace a given dude no more than once per turn.
So you can have Abram Grothe J , Abram Grothe (Experienced 1) K , and Abram Grothe (Experienced 2) K all in the same deck. But you can only swap them out for one level higher; you can swap regular to Exp 1 and then Exp 1 to Exp 2 (or either of the two in reverse), but not regular to Exp 2 (or vise versa). Also, you can still have experienced dudes in your starting posse or enter play even if you don't have the lesser experienced versions first; starting with Abram Grothe (Experienced 2) is totally fine.
Note however that one of the deckbuilding rules is that you can only have 4 copies of a card with the same title in your deck and as you'll notice: "Experienced X" is a keyword, not part of their printed title, meaning you can only have at most 4 total copies of any version of "Abram Grothe" in your deck. Also, the uniqueness rule applies: you can't bring Abram Grothe (Experienced 1) into play if the regular one is either in play or in Boot Hill.
(As a final note, sometimes tournaments will tie in with the overarching story and require you to only play the most experienced version of a dude or not allow dudes who have died in the story, but those are special tournament rules and not part of the default tournament gameplay).