The most rewarding way to do it is the actually play the game and earn them honestly. However if you want to unlock the weapons quicker, which I don't blame you for, then join an achievement server and go at it for a couple of hours, soon you will have them all unlocked, but remember to help the others in that server get their unlocks as well!
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Yes. TF2 is a GREAT game, and I recommend you "buy" it. TF2 is now free to Play.
No you cannot trade weapons for beta tf2 to normal tf2. Beta Tf2 is considered to be a completely different game by steam. Therefore the two game's inventories are not compatible.
Try lowering your graphics settings.
Weapons cannot be "leveled up" in TF2