Depends what you want to do. If you want to be able to emulate all the words of real languages, add the whole IPA system. If you want nice melodic options, add in accordance with your preferred music system (Asian 5 tone, Western 7 tone, Modern 12 tone, each with steps and variations, and repeating form 20 Hz up to 20 000 Hz) and for each possible sound humans can produce - different voiced and voiceless sounds, whispered (ha) or normal (a), and so on. If you want to actually use it and keep it independent of other languages, I suggest keeping it simple - a movie language, for instance, is more effectful if you only choose in-character sounds.
Btw, you get a lot more sounds even in English and Italian if you include unusual words, regional dialects and so on - a large part of the IPA phonemes can be used in either language, though people often don't notice.
Here a few different English vowels (all mainstream):
That's 32 distinct sounds. Some might be debatable, they are also dependent on dialect - "and" and "entity" start with the same sound for some, but I hear a difference - at least in some regions. The e in "Garden" isn't a sound at all according to some. And so on. The version on Wikipedia (English phonology) is slightly different. "Ha" is even in IPA written as two sounds, though it clearly is one sound (a whispered "a"), as you can see when stretching it, with or without adding a letter afterwards. I even ommitted a few vowels only the British/Australian/Canadian people use. According to Google, US English has 14-16 vowel phonemes, Australian English 20-21. And the whispered variety isn't even included.
If you multiply by three for tonal (add Up like we do in questions and Down like we do in some forms of emphasis or sounding defeated), you get 96. Asia also has a wavering tonal, but that can be emulated with two letters imo.
If you multiply by two for 2 different lengths, you get 192. If we ignore the h-sounds, we are still at 96.
So what you have is not that much.