At first I thought it was a simple question. It is not. It is a good fundamental one.
I do not remember who said that is better to master the use of a few fonts, than to simply use a ton of them... That is not the actual quote... It seems that I did remember the quote either Xo)
First you need to understand the categories fonts are divided into. That would be a long answer, so you need to do some homework. https://www.google.com/search?q=font+categories
But in general there are some elements that define this categories:
The serif (or lack of it)
The difference (or lack of) between vertical and horizontal strokes
The overall shape (circular, squared, oval)
The style... (oh god, this is too board... Decorative... let us leave this alone for a while)
One classical set of "book fonts" categories is
By how thin the font is and how thin the stroke is:
Extended, Normal, Condensed
Bold, Normal, Thin
And a lot of variations on some cases. Extra, ultra, black...
One personal way to arrange "script" fonts is:
Manuscript (Stylish fonts with thin lines, simulating the use of a soft calligraphic pen)
Hand writing (Architect type)
Historical (Medieval, celtic, "textura", pre-Gutenberg)
In a practical sense
1) Sans serif
Choose let us say just 9 Sans serif fonts. A good option is to choose one that has variations of weight (all the variations count as one) 3 for each category (You can repeat the same font on different categories).
Some that looks good on menus. Normally I choose one condensed here, so the menu can have a little more text.
Some for text, one would be verdana, and choose another two.
For titles, one very rounded and circular at least.
For web concentrate more just in titles.
Two Old Style
This works on long and small texts. There are not many to choose from. Choose just 2.
Be ready to have a long collection of Script fonts
But only collect them as the project requires it. Do not waste your time if you do not have a specific case.
Regarding your requirements
Just stick to the google fonts.
And I agree that "Novel" and "General Purpose" are contradictory terms. But I stated that on my "classifications" of fonts.