Unless you're *really good* at finishing projects that you start, very interested in fixing up bikes, and have the time planned out, don't pick up a "project bike" on the cheap. I told myself I was working on one I got for free for 3 years before I gave up and got one I truly liked and looked forward to riding.
It's not clear if you're actually in the red financially, but I would reason if you would ride a bike at all (as a commute or before/after/weekends/errands/ec), it is a good investment in your *health*. Do you pay for any unhealthy hobbies (Netflix, computer games, other sedentary entertainment, sweets or snacks?) I'm not judging, I indulge in those occasionally...but if I look critically at my priorities, these things would go before any fitness-related expenses (that I use). Once I adopted that mindset, I let myself rent a gym locker (gym was "free", as I'm a student) and buy new running shoes (so my shins didn't hurt) and hire a personal trainer ($15 for a half hour every 2 weeks) and replaced Hulu with Spotify (so I can have a constantly-rotating workout playlist). And you know what? I work out more now. I'm getting my returns for that money.
2 miles biking is an easy/short commute (that's what mine is), but it is noticeable. I also definitely agree with not setting a 5x a week goal off the bat. Give yourself a pat on the back for 3x, and extra props for 4x. You don't have to take your "day off" but things come up.
Good luck!