HASL and HASL-RoHS goes through a process when they actually use solder on the pads to "level" them. This can cause warping depending on how the manufacturer approaches it. This will leave small puddles of solder on all pads.
ENIG plates the pads in nickel and then plates in a small layer of gold, this makes the best looking boards, without spending the money for Hard gold plating, and it doesn't add solder.
The order you have them listed is from cheapest to most expensive. But I would recommend ENIG, hands down the best option.
There are quite a few prototyping services people have used on here, seeedstudio, easyEDA, and more.