Hi and welcome to HOD!
From your description, I would lean toward Little Hands to Heaven (LHTH), adding in Kinder math, phonics, and handwriting/fine motor skills as he is ready. The reason is that LHTH is a very good foundation for school on many levels and it is short enough to give you time to focus on some of those basic skills like reading, math, and handwriting (and plenty of time to just be a kid and explore and play too!). I'm afraid if you jump straight into Little Hearts for His Glory (LHFHG) it will be overwhelming, like Rice said. Plus, the guides get deeper and move challenging in just a few years...its very helpful to spend these young years laying that strong foundation.
If you do start with LHTH, don't feel like you need to start K options right away. It's okay to get started with LHTH and then add K math, phonics, handwriting a little at a time as you see he's ready...at his own pace. With my 5 year old, we started LHTH a little before he turned 5, then started math a few months later, then phonics a little after that. We still haven't added in handwriting because he is allergic to pencils (or at least he thinks he is, lol). Giving him a tad more time before jumping in to that. When people ask what grade he's in I never quite know what to say. Uh, half prek, half K. But that's the beauty of homeschooling I guess!
You can find those K options on the LHFHG page. In the LHFHG guide, Carrie includes hands on activities to go with the math workbook. They are helpful and fun (and often yummy). If you'd like to utilize those activities, you would need to purchase the LHFHG guide along with the math books. (They will still give you the package discount for LHFHG when you order that later...just tell them what you did).
These early guides seem very simple and with my first highly intelligent son, I was concerned they wouldn't be enough. But Carrie packs so much into the short school time, it's pretty amazing. She keeps a good balance and it encourages us to let our kids enjoy just being little!