How to predict which complex is formed and which are soluble?
Please be mindful, in my opinion, that your source material may not be of the highest quality.
For example, NH4OH is more accurately represented as aqueous ammonia (that is, NH3(aq), see, for example, this source's comment).
Second, Al(OH)3 does not form a complex with ammonia or, as your reference claims, is 'partially soluble' with aqueous ammonia to any significant extent, and if at all, likely due to the presence of OH-. See, for example, this ebook, Basic Analytical Chemistry
 discussing various metal compounds interactions with aqueous ammonia.
Third, a more accurate depiction of the action of ammonia on Cu(OH)2, for example, is the formation of a complex of the form, $\ce{[Cu(NH3)_x(H2O)y](+)}$, where x + y = 6, with also a possible charge of 2+ for cupric, where the concentration of ammonia influences the value of 'x' (supplying guidance on your question as to which possible complex may form).
Lastly, high strength ammonia is needed to react with some of the listed metal hydroxides and is characteristic of the particular metal. See my suggested source, that may address your question on which salts are (or, are not) soluble.