Dialect  closer to fusha it's shami "Jordan, Syria, Palestine"

Like this example

shami

كيف حالك؟

or

رجل

or

اسكت

fusha

كيف حالك؟

or

رجل

or

اسكت

khaliji

جوه؟

or

ريال

or

سك فمك /سك حلقك

I do'nt know why they say that khaliji is closest to fusha !!!!!!!!!!!!!!!!!!!!!!!!!!!!!

If you want to learn the dialect closest to fusha and help you to
learn fusha fastest the best choose is Shami

My suggestion is try to learn fusha(MSA) directly because you will face diffcults to find resources and records of dialects but standard one have thousands of books makes you learn qucikly 

Everyone will recommend his language, because it is easy to speak it:

Honestly:

1- Language of quraan is the fusha in its original version, clearly understood by the common arabic nations, and the science of arabic language 'nahu' is Deduced from The Quraan.

2- Egypt is the largest arabic nation, so that the egyptian arabic is the most spoken and understood, however you should learn the standard egyptian dialect, not other sub-dialects.

3- finally, Choose to learn the dialect of the lands you are targeting to visit.

Actually each dialect has similarities with MSA. but I think Yemani (spacially Taizi) dialect is the closet one to MSA.

I suggest you to learn MSA if you haven't learned it becuase by MSA you can contact with any Arabic man. But if you studied a specific dialect will be able to contact with people who speak this dialect and some people from nerby countries only =) 

I think that the closest dialect is the khaliji , and I also recommend you to learn khaliji dialect