I alternate between running and weight training; I do both early in the morning and work out every day. That said, when we had a newborn, it was tougher. As for what to do, I don't think you need to worry too much about that. Unless you have a specific goal, fitness is as simple as:
1. pick something to do
2. do it consistently
Or, to be even more succinct: Keep Moving
That said, sometimes the particulars can be hard to get a handle on. Given your life situation at present, I recommend finding something that's simple, efficient, and effective. Being able to do it without hitting a gym sounds like it would be a plus. I had good luck with Simple and Sinister, a basic kettlebell workout that is good for people new to kettlebells but excellent for anyone. One kettlebell and you're good to go. I also enjoy running, and it can be done with no equipment investment other than shoes. Finally, you may want to look at a bodyweight strength training workout, which also requires no equipment and can be done anywhere, anytime. Your Body is a Barbell is one I have used with good results.
Ultimately, you have to decide what works for you. For me, a consistent workout time every day is best, but you may do fine on a more ad hoc schedule. Whatever helps with adherence is the way to go, both in terms of workout frequency and in terms of the type of exercise you choose.