There are several surgeries available. The ones posted are just the ones that readers have had done lately. If you do a search you will find more.
I had the Toupet fundoplication. It's like the Nissen in that the fundus is used to wrap around the esophagus, but it's like the Hill in that it's a partial wrap, usually 270 degrees.
You should not decide on a particular type of surgery, or whether you need surgery at all, by yourself. The decision should be made by the surgeon based on the results of tests and what he sees when he actually gets a look at the situation.
My surgeon did my operation based on my very large paraesophageal hernia (stomach stuck in the chest due to a vehicle wreck), and also my completely
open LES, and my weak swallowing reflex. It was the right operation for me and 4 months out I am able to eat (except gas producing vegetables) and even burp a little.
Before you decide on surgery try everything else. Surgery is a last resort! If you don't have a fixed hernia or a really bad LES, you can probably do fine with just medication. I lived just fine on meds for 25 years even with a small sliding hiatal hernia. Surgery is not fun and there are some eating limitations that can continue for years. Many patients also need to keep on taking acid reducers after surgery.