3 days a week, using two 10-15 minute "PR zones" per workout, will be plenty to start with. That article should explain most of it (there have been a bunch of other articles about it too.) Basically, you alternate between two exercises for a specific time period, rest a bit, then alternate with two different exercises.
Your one and only goal is to do more reps in each PR zone every workout. Could be one more rep, could be 12. Whatever. It's an awesome combo of "pace yourself" and "push yourself."
With your equipment, some pairings I'd consider are goblet squats and push-ups (hands on the bench if needed); dumbbell deadlifts and resistance band rows; one-arm rows (left side, right side); and/or lunges (unweighted if needed, left side and right side).
Just to clarify, good training is strenuous. It's supposed to be. And you'll still get used to it. If it's easy, it's usually not productive.
A protein shake can help, but you do definitely need to clean up your nutrition no matter what. What, exactly, did you eat yesterday?
You basically want to burn fat and build muscle, that's what 98% of the guys here want. As a beginner, you can usually see progress in both directions, but depending on exactly where you're starting from (and how "borderline obese" you really are), you'll probably be better off focusing on a smart fat loss plan. You'll build strength and lean muscle along the way, but if you're that overweight, dropping fat should be the priority.
However, I must reiterate that I cannot afford gym fees. I can barely even afford to buy food, and pay my rent, which is more important than going to the gym. So I see working out at home the best way for me to lose weight, whilst saving money.
That's literally the first question addressed in the article I posted.
In the context of EDT, a "PR zone" is the 10-15 minute period that you're training, watching the clock, and actually getting your reps in. In that program, you keep the same weight for most workouts and you only increase the weight when you've gotten 20% more total reps.