How do summoning jutsus work?
Nope, it isn't explained at all.

The background you described is 100% filler and was never described in the manga, so using the Summoning Jutsu without a blood pact doesn't necessarily teleport you randomly.

As for which animal is suitable for which. Jiraiya seemingly decided to give Naruto the frog contract because he had the contract himself, (not to mention that Naruto's father, Minato, also had a blood contract with frogs).

I don't think there's a requirement of any sort, but that's just guessing. The entire technique is cloaked in mystery.

See my answer on this other question: How to summon a different animal using Kuchiyose?