Native speaker here lol. Standard English, from what I learned in school, is defined more by writing than speaking. In formal writing you always follow the conventions of proper/standard English. So the grammar you learn in a textbook is how you should be writing. Additionally, a thorough understanding of grammar allows you to take appropriate short cuts in writing. And the English used in England, the US, New Zealand, Australia, etc are all the same. The only difference is that the countries have different slang and colloquial terms, which you can't learn in a textbook. So I think the word "standard" isn't the right term. You use formal English for writing and formal situations, but colloquial English for speaking to friends and colleagues. Personally, and I'm biased, I think American English has the best slang and colloquial terms. But yes, in general, if a native speaker understands you 95% of the time when you speak, you're fine.

And please never use a Midwestern US accent or a southern one lol. You'll be more understood that way. Its probably the same in other english speaking countries, but definitely learn the dominant accent. Not understanding a native speakers English accent (bc of where they live) is a pet peeve of many Americans. But definitely expose yourself to the different accents of whatever English country you are interested in.