Many fish will exert severe behavioral changes if deprived of their common brethren, such as Danio Riero, with a group less than 5-7 the fish swim around like a goldfish… you get 5 together, they constantly shoal (school) across the top of the aquarium. For fish such as this, it would be strongly illadvised to purchase individuals…
However you’ve noticed people saying bettas are best alone, and this is also true. Male bettas are fighters with zeal! they’ll not stop till the other is dead if they’re put together, even so sensitive are their tempers that aquarium dividers do not always stop them from injuring themselves while trying to get through the divider and at the other specimen… For a fish like this you would seriously need it to be alone unless it has been conditioned for spawning, and at that… you’ll only give him female company for a very brief time period.
What will truly govern your choice of fish that you purchase will be the size of the environment you’re preparing for them… You are cycling your water right? (Google.com see: Nitrogen Cycle - Focus non-terrestrial). This is an imperative step to take before purchasing fish.
So if you have a 10 gallon tank or a 60 gallon tank, it will make a massive difference in which fish you buy. More than this, there are thousands of species, the better question should be… What are you interested in?
Feel free top pop me an email if you think of a fish in particular you’d like some info on.