trainers who definitely look like they know what they are talking about
This is NOT a good way to choose a trainer, there are a lot of people out there who may "look" like they know what they are doing but have no real training relying on "Bro Science" which is often useless or will lead to injuries in the long term. Never rule out an older trainer who may not have the "Perfect" trainer body as age, quality education and experience goes a long way.
For example, I no longer have the perfect body, Arthritis is a killer for your fitness levels, On the surface I may not look anything special (however my bodyfat % is quite normal and I carry a lot of muscle, but I am not "super cut" (maintaining super low BF% is not great for health anyway) I have over 30 years gym experience, I am not only a fully trained Personal Trainer but also a fully qualified Powerlifting coach, sports trainer (roughly equivalent to an Athletic trainer in the US) and massage therapist - I also keep up to date with extra courses and read studies, because knowledge changes. In Australia personal trainers are not covered by insurance to train people "beyond normal" so no bodybuilding or powerlifting etc. some still do train people that way but if they injure a client there is no insurance. Specific sports coaches are needed for advanced training. As a 46 year old woman i do not currently have the "trainer look" but that tells you nothing about past personal achievements, just by appearance alone you would not be able to tell that I am a former National powerlifting champion or that I have represented my country in another sport, or even that I missed Olympic selection due to a training injury in a combat sport.
So when choosing a trainer, ask about their training and their experience, do not rely on looks.
I want to start a program that could help me remove this excess of skin. A lot of friends and other forums reccomended to me some online programs but I don't trust to this things so much.
AS for books, there are some well known programs which are good to begin with eg. Beginner Strength or Stronglifts, but they are only a starting point. It is important to at least talk to a qualified trainer, individual goals, needs and health conditions are important to take into consideration and if you have never lifted before then you will need training in correct form so as to avoid injury. Learning form from random youtube videos is a recipe for injury.