Part of the problem is that most people have no idea how to do the basic lifts, and most personal trainers don't teach them. Another problem is a basic lack of structure, which is why I advocate focusing on the basic lifts: bench, squat, deadlift and maybe clean & press.
Doing both cardio and strength training is important, but I think most people already understand the basics of cardio.
For the average dude just trying to stay in shape, nothing beats the full olympic lifts. Take the barbell from the ground to over your head with snatches and cleans. Do it right and you'll be stronger than 90% of the people in the gym from 10 minutes three times a week.
FYI: The kind of lifts you see most people do in a gym are derived from body building routines, not proper strength training for athletic purposes. Such lifts will puff up muscles through sarcoplasmic hypertrophy. These slow movement high volume exercises actually decrease peak force, and puffed up muscles will slow you down and decrease aerobic efficiency. Hence the terms "blown-up" or "puffed-up" fighter.
Strength is more a neurological matter than people realize. Achieving higher explosive strength is almost more about training the nervous system than the muscles. The explosive lifts done properly achieve this training, whereas slow heavy-weight movements simply don't.
To equivocate, just snatches and cleans will lead to accommodation quickly. Variations will be necessary. But I will stand by my assertion that ten minute strength training routines done three times a week can leave you stronger than most of the people in a typical gym. You won't necessarily puff up bigger, but you will throw a much harder punch.
p.s.
I like how you admit to being a newbie elsewhere yet you're contradicting me with confidence. I'm not just talking out my ass. This is knowledge I use to win in the ring.
I wouldn't focus on being a certain weight or losing a certain weight - you should initially be staying about even since you will be increasing muscle mass while reducing fat mass.