It's understandable that you don't want to start over if you have at least 1k score, but any less than that, that is an option. By the time you hit 10k and beyond, you will look back and regret on the time wasted for a single weapon.
Bronze league is the best way you can get any rares you want. However, while farming bronze, instead of constantly thinking of a single weapon, you should simply think of collecting the rares you will need in the future. This is because
1) With an unupgraded deck, you may have a hard time getting 6 wins in a row.
2) Now with shards included in the rares, it is difficult to get the weapon you really want.