6 Most Venomous Spiders in the World

Loxoscles reclusa are pathetic. I wouldn't rate them in the top twenty.
Cheiracanthium (yellow sacs) are barely even a threat to flies. They have a rather mild venom, and I think I'd know because I've been bit by some at home quite a few times.
Any Latrodectus (widows) are somewhat dangerous and shouldn't be played with even though they rarely bite.
"Funnel web" is a term for many species of spider. Members of Agelenopsis (grass spiders) are what I would call a funnel web because of their web structure. Atrax are the Australian funnel webs and are quite dangerous, but the tale is longer than the beast.
Mouse spiders are generally not bad at all because they don't often bite as mentioned, but they also don't have too severe of a venom.
"Brazilian wandering spider" is very broad because there are many wandering spiders, but the genus Phoneutria is the one that is most dangerous. Even within the genus only a few are significant. I know a few people who keep some and they aren't that bad. The banana thing happens rarely and most spiders found on bananas are Sparassids (huntsman) and are medically insignificant.

While recluses are known for the "bite" that causes necrosis, it is uncommon to say the least. Typically that is the result of incorrect wound care. If you can wash it out and keep the area clean bacteria will not affect you much if at all. You can get the same infection from any puncture, cut or scrape if left untreated.