I say, first try to find a bicycle co-op in your area. Next, after you join the co-op, have a co-op mechanic evaluate your bike. Then discuss with a co-op leader the various components that need replacing and how you may best obtain those parts. After you've replaced the needed components, then address the new tire issue, along with the other minor concerns.
You'd be surprised at the difference new tires, rack, grips, and a saddle will make.
You're gonna need a decent U-lock, as well....
Last edited by WestPablo; 06-04-14 at 03:44 PM.