I am going to buy some stuff for a premium account. However, I do not want to buy an item that is possible to get through achievements because then that is a waste of money.
What are all the items that I can get through TF2 achievements?
You will find a full list of all achievement rewards at Valve's Team Fortress 2 Wiki. Some are dependant on character milestones, while others rely on events that may be locked out. Several come as rewards for unlocking achievements in other games, on Steam.
Character milestone rewards are unlocked for completing a certain amount of achievements in the respective class achievement category. I have included a link to each achievement list in the class name.
Halloween Rewards unlock by completing certain achievements within the Halloween maps and events. Most are more accessible during Halloween, but can still be unlocked throughout the year. Simply join a server running the appropriate maps.
These achievements relate to content updates and various other additions to the game.
These items are earned through alternate Steam titles.