Just to chip in with some personal view and current experience on this.
All respect to other posters like the prof who are very clear on where they are going and i can understand some of the frustrations coming out a bit.
Also--and once again (apologies) read this through 'beginner' filter as i don't pretend to be anything else.
I came into this just 18 months ago age 52, very overweight, very weak. I am not sure what my body fat % was back then although i would estimate somewhere up in the 35% range.
At that time i didn't even consider working out with weights (long term back injuries) but just aimed to shed a whole load of weight which i did with a solid outdoor walking programme and some sensible eating.
Now--just 8 months into working with weights for the first time i am just getting my head around a lot of this kind of discussion.
Most of the guys around here argue very strongly (and reasonably) that you can't do 2 things at once ie can't lose fat and get significantly bigger/stronger.
Except maybe you can as i am doing--but once again that is as a beginner and i am clearly doing both : still making beginner gains and still changing (slowly) my body composition.
Now : i am nowhere near where i want to be with either strength gains or body composition so i have just had to make a clear decision yself about which way to go ie simply get stronger and support that plan with the appropriate training and diet or aim to shift body fat quickly and support that plan with appropriate training and diet.
Although still relatively (even absolutely) weak by most T nation standards i figure that while i am still making beginner gains i can afford a quick hard cut of body fat , i can hang on to the strength gains i have made while gatting rid of more flab.
I have no pretensions to being a bb er ,whilst having huge respect for those that do, nor do i want to be a powelifter/strongman--what i do simply want to be is a maximally fit , lean,and strong old git !!.
I think that it is absolutely necasary to sort out in your own head what you want--i actually had to sit down, work it all out, tease apart all the elements we talk about in 'fitness' and start to work towards actual goals.
Some of them (i think) can be done together (for a beginner) and for a while, many require a clear direction--at least for a while.
Once you set goals--and can work to a plan that supports those goals..then you can get somewhere, might be lower bf ..nothing wrong with that...might be faster over 1.5 mile run, stronger on the big lifts, doesn't really matter but you must have YOUR goals.
Sorry if this didn't come across as clearly as i hoped.