Which border crossing is recommended? How long is the whole process?
There are 3 border crossings, just the Allenby/King Hussein is closest to Jerusalem and Amman, and transportation to there is simple, as there are direct shared vans that go from Golden Walls Hotel, which is next to Damascus Gate/Shar Schem/Bab El Amud in Arabic.
King Hussein has about 4,000 people crossing in each direction each day. And then you need to wait for a shuttle bus to take you between the terminals of Israel and Jordan. (It's no man's land in between, you are not allowed to walk it)
The other two border crossings are usually very fast, as passenger volume is very low, especially by Yitzhak Rabin Border Terminal 10 minute drive from Eilat, and then you cross over to the Jordanian side by foot. The other border crossing is Sheikh Hussein Bridge/Jordan Valley which is 10 km east of Beit She'an.