This is going to depend on your fitness level and goals...

I've been couch potat'ing for long enough that the C2K is actually a pretty hard workout.    I just completed W3R1 and the next day my legs muscles have had a healthy ache in them.   Adding squats and powercleans probably wouldn't add much to my rate of improvement and might very well leave me with an injury.

If I had started back into weightlifting 6-8 weeks ago and was a novice I'd probably spread the workload over the week by alternating days.

If I had been weightlifing for a year and was bordering on being an intermediate lifter I'd probably do my 30 minute runs on the same day as my lifting so that I would ensure adequate recovery times between workouts given the significantly higher workloads involved.

Today As I'm neither, I'm perfectly happy running the C2K without lifting and then adding in 3x/week lifting program while maintaining a steady state 5k - 3x a week program for for another 8 weeks to build a bit of a running base and a weightlifting base.

I'm more interested in strength and short distance running than ever running a marathon so my path would be to work up to intermediate strength levels and whatever a Hidgen 5k intermediate running type program could get me to.

just my thoughts, YMMV

I am starting today!  I have run off and on for years, but have been off since last summer.  So, it is starting over!  I am looking forward to this community of C25k!