Your questions are completely contingent on their nature to begin with.
What is your price budget?
What type of eel are you referring to when you say "an eel"
My Gymnothorax favagineus is most definitely not a messy eater in the slightest, stays in a cave all day, comes out at night and swims all over the place. My adult Gymnothorax favagineus IS a messy eater, stays in one place for 12 hours, moves a little in the night and repeats the cycle.
A "filter" is not a luxury for a saltwater tank.
You could very easily get a small snowflake eel (3-5inches) and house him in a 20 until he is 7+ in which case I would recommend a 40, from 7 to 10 a 40 will suffice but eventually you will need a 55+ for an adult SFE.
This is all naturally based on the fact that "an eel" is indeed referring to a SFE. My previous Gymnothorax Funebris, was quite the opposite of a calm fish. Not that he was aggressive but, he would swim a lot and eat very messily.
So it boils down to this.
You can surely get an SFE if you understand that in a short time you will have to make several tank adjustments, as far as size goes, and have proper media filtration, and habitat. Eels are hardy, fun, and loving pets, but need to be cared for properly.
A SFE that is 15 inches long and is in a 20 gallon will not thrive.
and remember in this hobby, fish need to THRIVE not Survive.