You can do -a lot- with body weight exercises, which still falls into the category of "weight lifting." I would recommend getting one of those Iron Gym Pullup bars if you don't have something you can easily do over/underhand pullups on, and then you can honestly get away with lots of bodyweight stuff (in the interest of losing weight, specifically) without getting crazy or having to go to the gym. I have a bench/power-rack combo in my apartment, so I haven't seen a gym in years. But it is a -sizable- initial cost, and you have to buy the rubber floor pads and all sorts of shit, not to mention that even at a discount, weights are just generally kind of expensive to purchase. Especially the coated ones for doing deadlifts etc.
What I do, at the end of every workout day (I do 3x a week for an hour solid, with like 30s max between sets/exercises. I'm half-assedly german volume training on top of supersets, with one rotating "heavy" day a week where instead I do a big push for numbers to check my progress) Is do a plank for as long as I can hold it (up to 4 minutes, used to be 7 but I got fat in the last 5 years) and then do Oblique Raises (elbow on ground, legs straight, lift so that those are the only two points of contact. Push opposite hip as close to the ceiling as you can get it, and hold for as long as you feel is good. I'm up to 45s on each side, because I have shit for core) and repeat 3x. I'm not a huge fan of crunch movements, because of the lower back strain, but they are definitely something you can do if you don't do full "situps" which are shit.
I'm not a fan of cardio, but if you must do cardio, I recommend either HIIT (which is most definitely not for everyone/beginners) or cycling at a solid pace. Depending on my mood, I might mix in a day or two of 15mph cycling over lightly hilly terrain. But I would definitely not recommend doing cardio on the same days you are doing lots of lifting type exercises. That's just a sure way to fuck up your mentality because you -will- not be as good lifting if you do cardio before, and your cardio after will seem slow and shitty because of the lifting.
I'm sure it's been covered 8 million times so far in this thread, but diet is like 90% of losing weight. If you can't keep your caloric intake below your usage, you won't lose weight. It's that simple. No matter how hard you work out, if you eat like a Body-Positive Advocate, you're going to be big. And not in a good way. The Chicken/Rice/Broccoli thing is a solid starting place, and just do some research either using google or the fda food website to try and incorporate other light meals into your day.
Skipping a meal for a shake requires that the shake supplies everything that a meal could, which is difficult if you aren't supplementing the shit out of your shakes. I skip breakfast but I have a hefty fucking shake with protein powder, peanut butter, oats, ginger, and a banana in it each time. Then I generally go salad/fish/chicken/whatever light for lunch, then I'm usually set for whatever I want for dinner unless it's something ridiculous like pasta alfredo or anything that involves cheese. I gotta do some pretty gnarly lifting during the day to get to cheese-centric land, even though I love it =|