>>4 While it's true that katana can go up to $3000, the average price for a custom handmade sword is 1200$. You can also purchase a custom handmade iaito (not sharp) katana for 600 dollars.
I'd recommend the bokken (wooden training sword) which is 10 dollars. It's durable and safer for a beginner to use.
After using the bokken for a about 6 months or so. Move up to the iaito. That way you can have a better feel for an actual katana. Also you reduce the risk of cutting yourself upon opening the katana.
( yes if you use improper technique when drawing your sword, the scabbard will ware down and eventually break. A lot of amateurs lose fingers because of this. You could also get a metal scabbard.)