The cheapest option is going to fix the current bike's issues.
That said, that isn't what you asked for. Without knowing what you use the bike for, my standard answer would be a fitness hybrid like the Trek FX series. Fast enough for long rides but easy to add racks, fenders, and all sorts of commuting gear. Many used models will already have the accessories on them.
I have a 7500 FX I got used for $250. The minimum model brand new would be the 7.2, which is between $500-$600.