I have mastered the British accent spoken by the upper classes in Britain. It is called Received Pronunciation (RP).
Then I went to the USA, New York and researched American accents. What I have found out is that the most sophisticated General American accent is close to British RP.
I personally prefer British RP as it is regarded in the world more, but if you plan to live in the USA then I recommend that you master the General American accent. When I was in an airport restaurant in New York and asked the waiter to bring me a fork, he could not understand me as I pronounced it in the British way. In the word “fork” Americans always pronounce the /r/ sounds whilst in British RP it is not pronounced. Also in the long vowels /ɑː/ as “car” and /ɜː/ as in “Sir”, and in the three diphthongs /eə/ as in “pair”, /ɪə/ as in “ear”, and /ʊə/ as in “sure” the ruling applies.
Another point is that British English is more crisp because in RP consonants are well articulated. For example, in the American accent where the /t/ sound is between two vowel sounds as in “later” is pronounced as a fast /d/, in British RP it is a well-articulated /t/ sound.
I have developed and published apps for both British RP and General American pronunciation.
You can master which one you need with the apps Elocution Lessons, Get Rid of your Accent UK1, Business English Speech and Fluent English Speech (British English) or American Accent App and Fluent American Speech (American English). There are also two accompanying video courses: Get Rid of your Accent Part 1 and Get rid of your Accent Part 2.
The same apps are also available on Google Play. They are based on the bestselling books in the series Get Rid of your Accent and have audio and recording buttons.