I would avoid TM. I haven't done much research into it, but the little I know suggests that there isn't much there that isn't available for free in many, many other formats (books, apps, podcasts, local groups (sangha), etc.). I've seen a lot of criticisms of it as well; I'm surprised you haven't.
I am a deeply skeptical person and didn't give much thought to meditation, but started to see it popping up in some of the science/atheist/skeptical books and podcasts I follow. I'm now convinced by the weight of the scientific evidence as well as personal experience that there really is something to it, although for me the effects are what I would label mild-moderate.
For me, mindfulness meditation has stuck pretty well. This is largely due to two factors; first, I spent a *lot* of time researching the science behind meditation and it convinced me that there is both evidence supporting its efficacy as well as some plausible biophysical mechanisms for those effects and second, it seems to have completely cured my lifelong depression. For me the critical step was the abundance of research that's showing benefits, although there's a lot more research that needs to be done. I don't know what would make it stick for you. For some people having a community helps something like this stick, but for me it's a detractor. I have not found any remotely like-minded people in my local meditation community and honestly am really put off by the Buddhist/spiritual mumbo-jumbo that many meditators espouse.
If you want it to stick, I would google "how to form a new habit". There are plenty of tricks you can use, like doing it at the same time each day, making a 30-day or 6 week or whatever commitment, etc. The only things that I would say are unique about meditation are that most people have a very incorrect view of what meditation actually entails, people think you need to do a huge amount to get benefits, and people don't realize that there are many different styles of meditation that have different benefits. There's evidence that just short periods of time (5/10/15 minutes per day) provides benefit, so don't kill yourself trying to meditate for an hour. That would be setting yourself up for failure. I would then try to target the benefit you're trying to get from meditation. If you want to "clearing a noisy mind" as you mention at the bottom of your post, then I think mindfulness meditation is probably what you want. Sometimes mindfulness meditation is mis-characterized as Vipassana which is actually insight meditation, but because Vipassana usually starts with mindfulness as a first step before really getting into Vipassana itself you can sort of use the two interchangeably at the beginning.
My favorite book on the subject is Fully Present: The Science, Art, and Practice of Mindfulness. Dr. Smalley is a Biologist who (as she describes in the book) was a hardcore skeptic about meditation so it really spoke to me. I like that there are a number of exercises you can easily find depending on what you're looking for.
In my experience, most people who I know who have started to meditate have seen some benefits starting after about a month or six weeks of 10 minutes a day. That aligns with a lot of the studies that have been done as well. I'd suggest doing some research into how to meditate, and maybe download an app. I like Joseph Goldstein's 5-60 minute "Mindfulness Meditation" on the 10% Happier app (mostly pay, but that meditation is free) or Tara Brach's "Vipassana (Basic) Meditation" on the Insight Meditation Timer app (free). Both provide good, simple instructions.
Feel free to ask more questions on this thread or send an IM if you prefer.