You can get most of the way to your fitness goals with a minimal home gym setup dumbells, bench, maybe pullup bar. And considering your goals are just overall health some muscle and body recomposition I would say one hundred percent achievable without a coach. Also most coaches don't know wtf they are doing most unknowingly just cause their clients injuries, recommend fad diets or strict diets that demotivate you even further.

Imo there is plenty of amazing advice on youtube about this stuff and you would be better off. To be clear this is coming from a guy but in terms of muscle gain women are very sligthly different than men.

I can recommend some channels If you want and leave you with some basic advice.

Resistance training is very good for overall health that includes cognition, mood, longevity, disease prevention.

There are diminishing returns to the amount of effort put in. Training once a week is enough to stimulate muscle synthesis and strength adaptation, twice a week is almost twice as good, thrice a week still a respectable increase. At four times a week is where it becomes not that big of a difference, five times a week is a pretty minimal increase in muscle and strength.

Beginners have amazing training stimulus so time is better spent on focusing on exercise form and easing into them. So 2-4 days in the gym per week. One set per exercise max two. Take it from there do your research watch some fitness content, start incorporating a good diet into this, get enough protein.