So I have an 09 Fuji Track and I want to get a new crankset. From what I have found my bottom bracket length is 103mm and most of the affordable cranksets I have found require a larger bottom bracket, so I would need to upgrade that? If I get a different sized bottom bracket does that mean I have to change my cog at all so the chain is straight?

As well I want to go down from 48 teeth to 46, does that require shortening the chain as well?

Any info on this topic would be great and even crankset suggestions in the 100-150 dollar range would be helpful as well, thanks.