Although I think its a good idea to be inspired by successful writers of the past and present, I would caution against writing "like" any of them. As you fear, you run the risk of sounding dated, but worst yet, like a soul-less copy cat.
You've brought up two very different types of writers. Specifically, Hemingway, one whose work has been critically acclaimed and won numerous literary awards for it's subject and skill and the other, Meyers, who has been criticized for her lack of literary skill. Both however, have experienced great success and it's important to understand what you should be influenced by.
These writers have experiences, perspectives and most importantly, capabilities that helps create the authentic styles that are uniquely theirs. And that is what brought them success.
Hemingway wrote as he wrote and Meyers writes as she writes because of their capability. Meyers is heavy on the purple prose and is at times considered lazy about her overuse of the same words. She's more focused on creating a world full of characters you think you know, rather than how she conveys it.
Where you consider Hemingway's writing simple, it really is more curated, meaning every word on that page carries all the weight it can handle so he conveys everything he wants you to know and feel with as few words as possible. Two very different approaches.
Meyers couldn't write like Hemingway if she wanted to and visa versa. They come from two different worlds which brings us to:
Hemingway wrote for his school paper, went on to work for the Kansas City Star, which is said to have been a major influence in his "distinctively stripped-down prose."
He once said, "On the Star you were forced to learn to write a simple declarative sentence. This is useful to anyone. Newspaper work will not harm a young writer and could help him if he gets out of it in time."
He also had the privaledge of having a great mentor and being in the company of other great writers such as F. Scott Fitzgerald, Ezra Pound, Pablo Picasso before he started his own career. As with anything, learning from the best puts you at a great advantage and he was surrounded by greatness even before he put pen to paper for his first novel.
Meyer's worked as a receptionist in a property company before she jumped head first into writing her novels, the Twilight series which was inspired by a dream. Meyer loves the work of Jane Austen and has been inspired by several other classic writers, but you will notice, none of that old-style can be found anywhere near her writing. Just the essence of heavy description and ideas.
She simply isn't a literary genius, but that isn't her path, and that is okay. She found her lane and she is killing it.
Meyer says her faith, as a straight-laced member of The Church of Jesus Christ of Latter-day Saints, heavily influences her characters which is apparent in her themes of purity and light.
Hemingway on the other hand experienced war, traveled the world, engaged in adventurous and sometimes dangerous activities that enriched the world's he created. Without his experience in war, we don't have the Sun Also Rises and Farewell to Arms.
They write what they know and that is the basis for their style and voice.
Your focus needs to be on what your personal capabilities are.
If you haven't already, start working on your novel/short story ect, without worrying about what you're jotting down.
In the editing phase, take a step back and see what natural writing pattern emerges. Is it simple and punchy and or purple and flowery with big words and long sentences? Maybe it's a mix bag and you've come up with your own distinct style that some kid will be thinking about 50 years from now.
Ultimately, your influences and experiences will help color in the rest, as it is your perspective that will determine your voice and style.