Over the summer, I was in my school's weightlifting program. Varsity athletes are required to take it, but I'm not an athlete, so I just took it for my own benefit. Anyhow, we would start the day by going outside and stretching and doing warmup exercises (jumping jacks, pushups, situps, etc). Then we'd jog around the track for about 1/2 a mile and immediately go inside to lift. We'd have to get 1 set in before he let us get water (i don't know the reasoning behind this...).
On some days, we'd do sprints and these "ladder exercises" where you step in and out of a plastic, rope-like ladder. We'd combine that with medicine ball situps and other things. On those heavy aerobic days, we didn't lift much if at all.
I personally benefited very much from this kind of workout. I put on muscle fast and the aerobics burned off calories. I followed the dietary guidelines and in 2 1/2 months I was transformed. For those of you that want a good six-pack, I REALLY reccomend the declined bench. Use that thing with weights and try to hold some of the crunches for 10-15 seconds. WOW, the first time I did those, my abs hurt for 2 days, but it was worth it, haha.
So to answer your question directly, running before lifting isn't bad, just don't overdo it. A mile sounds a bit much to me.
