First, I suggest you leave KJV Onlyism without leaving the King James Bible. The KJV offers translation choices and unique sentence structures that will only enrich your study of Scripture. The differences between it and whatever version you choose will prompt you to consider passages deeper than you otherwise would.
Second, it depends. I usually recommend Bibles on a case-by-case basis. For example, I may give an NIV to a young person who is new to the faith since it’s easier to read than some. But I may hand someone like you a copy of the NKJV or MEV since they are the closest parallels to the version you know best.
Bible translations primarily differ in two ways: source material and translation method.
Concerning source material, the KJV stands apart from most modern translations because it is based on a handful of later manuscripts, that is, hand-written copies of the Bible in its original languages. Today, most translations use much older and considerably more manuscripts to which the KJV committee didn’t have access.
Moving from the KJV to a modern translation means you’ll likely find a few textual variants. You may see an extra word. Perhaps a verse is missing. There are reasons for these differences, namely, the manuscript evidence supports the changes from what we read in the KJV.
If you’re willing to accept the existence of these variants—there aren’t as many as you may think—and even strive to understand them better, I recommend the ESV, English Standard Version. Arguably, the ESV is a direct descendent of the KJV, retaining much of its prose and cadence.
If you’re not ready to step quite so far from KJV Onlyism, you should try the MEV, Modern English Version. It’s a modern translation of the very same manuscripts as the KJV.
Translation method is the other factor to consider. Some Bibles are more literal translations than others, not that literal is necessarily better. In most cases, I’d argue for the essentially literal version rather than one that paraphrases some of the text. Then again, technically, they all paraphrase.
The most important feature of any translation is how well it communicates God’s word to the reader. A so-called “dynamic” translation could be more effective than its literal counterpart.
The ESV is just as literal as the KJV if not more so. The NIV, New International Version, is not quite as literal but a slightly smoother read for 21st-century Christians. If you want to split the difference, the CSB, Christian Standard Bible, is an excellent option.
The choice is yours to make, of course.
Personally, I use the ESV as my standard, but I’m never without other versions when I study. My collection also includes the NASB, KJV, NKJV, MEV, HCSB, CSB, NIV, NET, NLT, and a handful of others including some that were published before the KJV.