Need advice onan at home work out routine please

For the last couple months I have been trying to get back into exercising but starting this week, my goal is to stay consistent at least 4-5 days a week. I have got to lose some weight.

To start, I am trying to set up a better exercise plan. “Exercise with a purpose”. I can only work out at home in the mornings before my daughter wakes up, but I have a treadmill and a few different dumbbells. I have been trying to read into plans / work out suggestions but I’m still not sure if how I want to set up my work outs are ok. I’m mostly worried about overdoing it on my lower body.

I know strength is important and I want some of that in my plan but my biggest focus right now is cardio / running. I like it; I like trying to beat my times / distance and I really need it to try and speed up my weight loss.

I was hoping to run Monday, Wednesday and Fridays (I’m still working on getting better so it’s more like a jog with some faster minutes in between). Before getting on the treadmill, I was planning to spend 30mins doing core and upper body. Then 30mins on the treadmill.

Tuesdays and Thursday’s I was planning to work on lower body and no running. If anything maybe just walking 30mins to cool down.

I keep reading about giving your muscles time to rest and heal. I’m wondering if my plan is too much on my legs? Or if this really is an ok / good split? I’m on Pinterest and reading blogs a lot right now but would really like some helpful input on what I’d like to try and do please