I have a 30 year old copy of Hanon, which I only worked right through about 3 years ago. I try to play the piano every day but only in the past week got the opportunity (and speed) to play through all 60 exercises every day.
Most of the criticisms of Hanon seem to be aimed at part one, the first 20 exercises, which are repetitive, but are meant to prepare you for the other two parts which include longer exercises, the major and minor scales (all one exercise), arpeggios, scales in thirds and some brilliant trill and tremolo exercises.
I play publicly in a church for worship and in a Jazz band. When I play Hanon I receive more compliments on my playing, both from the public and peers. It's as simple as that.
When I practise Hanon, I feel my playing is sharper, freer and that if I feel inspired to play something I am more likely to be able to play it and not as restricted by technical or physical limits.
I doubt you're going to rush to a teacher now, so I would recommend you start slowly, follow the written instructions and fingering, observe qualified pianists on Youtube etc to copy their technique.
Don't rush to play through all 60, but adopt Hanon as a habit, play for whatever time you can allot to them every day and impreove technique and speed naturally.
I describe Hanon exercises as "boot camp for piano". If you are attracted to them then go for it, but observe the same level of care as if you were going through an assault course. In return you will improve directly and collaterally, in technique, reading and facility in different keys. (incidentally, playing the exercises in different keys takes you up another league).
The advice below is exactly what I tell my pupils:
Play gently and carefully. I have two, one has been with me for 10 years, is learning for fun, has relatively little time to practise, but uses it diligently. For her, the Hanon's 60 is a useful repository of scales etc in one place, and I can call on specific exercises to tackle particular that arise with technique etc. Once a year or so I ask her to practice through the first 20 exercises just to cover the ground.
The other pupil started recently and wanted to progress as quickly as possible. He is diligent, practises for an hour or more at least 3 days per week, as work and voluntary activities allow. Using the 'boot camp' principle, After 9 months he can now play through the first 20 exercises in an hour if he so wished. He has been using a beginner's piano book to get the hang of playing tunes and is studying a music theory book alongside all this. He is about to begin learning his first Bach invention.
If I change my mind about using Hanon I'm not to proud to say so, but so far it's a useful tool, and like all tools needs to be used appropriately for the job.
I have just finished playing through all 60 exercises in 1 hour and 20 minutes. Last year as a result of playing the acoustic guitar for a 6 hour live gig on St Patrick's Day using poor technique and inadequate amplfication, I developed RSI in my left hand and a pain in the base of my thumb. When I practise Hanon every day the pain disappears. I'm not saying it's Hanon specifically that does that, but that it seems to be no more harmful than other approaches and readies me to play the improvisations I would like to play from my head.