I'm going to go on a rambling post and cover too much in the scope of a forum post, but the crux of the matter is that in order to lose weight and become more healthy, you need to establish new habits that discourage old habits.
The first thing is establishing a clear and concise goal. If you want to be able to plank for 5 minutes, that's a clear and concise goal. However, having goals like "I want to be more healthy" are kind of vague, but you can work with those if you clearly define how you plan on doing it.
This past year, I decided to make a meaningful change in my life to try to lose weight (because it's cheaper than aluminum suspension components and slightly healthier). Instead of coming home, making a large dinner, and goofing off throughout the night, I now come home, unwind for about an hour, and then head to the gym. Every weekday, and I have to be sick or have something out of the ordinary show up to not go. Even if I wasn't feeling it, I still went to the gym and did laps for 15 minutes. Just the physical act of displacing myself from my house has helped a bunch, there are some days where I really don't feel like doing anything, but I go to the gym and actually get into it and have a good day at the gym. It's a lot easier to convince yourself that you're tired and you don't feel like running or lifting a heavy ass weight if you're nowhere near where you do that stuff, but if you make it a habit to go to the gym, just the sheer proximity will make you want to do a few laps or lift.
The programs that I used are well known (Starting Strength & Couch-to-5K), and I had done them in the past, but I would run out of steam in 8-12 weeks, and then gain back all of the temporary weight that I lost. The only thing that's changed is going to the gym extremely regularly, and I've been losing my mind since the NC State gym has been closed since Christmas Eve. It sounds nuts, but you can get to a point where you miss being a sweaty mess, and it's all via habit. At the beginning of the year, I could probably do 1 or 2 dead hang pull-ups and struggle through the entire range of motion, I can do 10 in a row reliably with no breakdown in form at any time.
The plank challenge sounds like a good starting point since it is deceivingly difficult; however, I'm weary of stuff like that and especially the ab challenge because it's kind of gimmicky. Doing crunches and sit-ups are actually really bad for your back, and if you want to have abs it's determined by your body fat %; however, if you want a stronger core, planks are a really good way to go about it. Unfortunately there is no substitute for hard work, and a few minutes a day of just doing planks probably won't get you the results you're after, but it's a start. I'm just weary of fitness programs that don't have a defined progression past whenever the prescribed program ends. For example, Starting Strength can be rolled into the Texas Method or a 5x5 program and Couch-to-5K has Bridge-to-10K (or you can focus on getting your 5K times down).
If you really want to go nuts, you could always join the ranks of cyclists we have within THSCC. It could be slightly cheaper than buying E36s, but the price floor on those has really dropped in the past few years.
