When using the Steam Community Market, it says I am unable to sell items because "...we require that users have made any purchase on Steam in the last year, the first of which mus have occurred more than 30 days ago." I know I could simply buy a game to satisfy this requirement, but my question is whether or not I can buy an item in the TF2 Mann Co. store instead.
Any purchase of a game or currency/content within a game (using Steam funds) constitues the requirement to sell items in the Community Market.
In your case, if you buy something from the TF2 in-game store (or web store), yes, you can sell items on the Community Market.
If you purchase any game from Steam by depositing money in your Steam Wallet then purchasing any game, the same also applies.
Let's look at their Trading and Market Restrictions FAQ:
An account must be trusted in order to use the Community Market. To be trusted, the account must have a successful purchase older than thirty days, but not older than a year. The purchase of wallet funds qualifies for becoming trusted.
Therefore you could buy from the TF2 store, as long as you did so by adding funds to your Steam wallet (which I believe is how it's done anyways).