One more “yay, you!” to the chorus. And it’s only January, dude - you’re already seeing results! You didn’t get out of shape in two months, you won’t get back in that fast either, so seeing some tangible results is a great thing! It might help to set a little Outlook reminder to ping you - Outlook is unflagging and is always motivate to tell you to go walk around! 
Anything you do is better than not doing anything at all. (Exercise-wise.)
A small point, but I disagree with this. I think you become less efficient as you get tired. A fresh person will take nice, quick, smooth steps, using mostly their legs. As they become tired they begin to ‘cheat’, possibly swinging their arms, swinging their upper body, or maybe using the railing more. This is less efficient, but transfers some of the effort from the tired leg muscles to other less tired muscles.
The simplification is more than adequate to the question, and the difference is small enough in a practical sense as to be irrelevant to the practices of a person trying to lose weight.
The most important thing about exercise is actually doing it. Park in the most distant parking spot, walk half way up the stair before taking the elvator. It’s not sports, but it helps. Then add more, every time you do it. even if all you can add is taking a lap around the car before you walk in, do it. Next day, walk two steps up, one step down on the first flight of stairs. Third day, . . . etc.
If you can find a place to swim, it’s a great idea. Indoors, so you can do it all year. If half a lap of back stroke is all you got, do it. In six months you will be doing a lot more. Swimming is almost no impact on your skeleton. Just be sure you increase your total activity every day by some trivial fraction. Don’t discourage yourself by setting silly goals. (OK going out on the walk to end breast cancer so you can walk with girls is a worthy goal. Try the Three K first, though.)
Getting out of breath is a good idea, but even that is not essential. I found that the stationary bike for five minutes, and then a walk is best for me. Gets the heart rate up at the beginning, then walking keeps it elevated. The bike alone is too damned boring, and I know I won’t keep it up.
The other thing about goals is that you meet them. Turns out us fat lazy guys stop doing it after that. :smack:
Tris
That’s a pretty good writeup, actually, though given the audience it’s obviously written with a bias toward endurance running.
Whether you’re looking for overall health and performance or than training for optimal performance in a specific sport, you benefit from variety. Endurance athletes see performance benefits from strength training and explosive-power efforts like sprinting or Olympic lifting, while athletes who do mainly strength work should be putting in at least some time with endurance protocols like HIIT to build capacity and endurance.
Don’t remember who said this quote, “The best workout is whatever you’re not doing,” but it’s pretty apt. Your body gets better at doing whatever you do often. Experienced athletes sometimes become overly-adapted to their particular exercise. This can make you more prone to injury, or become unable to perform well in certain capacities. Some elite distance runners literally don’t have enough leg power to skip steps while running upstairs. They’re so adapted that their vertical leap in inches is measured in single digits.
If you’re talking about someone who’s so sedentary that going up and down a few flights of stairs qualifies as a workout, all of this is pretty irrelevant, I’ll admit. It doesn’t matter what you do if you’re untrained, you’ll get some benefit from anything you do. No exaggeration, if you took up yodeling practice for 30 minutes 3 times a week, and juggled on the off days, you’d probably get an increase in fitness.
Bang for your buck, though, strength training with some short-duration medium to high intensity “cardio,” or strength-endurance work will get better results for the time spent than just about anything else. Straight endurance work is not the best use of your time if you want to increase your fitness level. Life is primarily a strength-endurance event; working in your garden or cleaning out your garage has a lot more in common with doing something like a bunch of burpees than it does with running several miles.