Hi, Wendy. Welcome!
I've always believed in planting
transplants deeply, and I still do. I think it makes it easier to maintain the plant throughout its life-cycle, especially when we're fond of keeping them up off the ground. However, plants that sprout on their own and are left to sprawl seem to produce just fine too. They might do this because they never experience transplant shock and those that are left to sprawl will make new roots wherever their branches touch bare soil. When we tie them up off of the ground they can no longer do this for themselves, so that's where it's most helpful to plant deeply and get more roots straight off of the main stem.
The best thing I've learned lately for growing very fruitful tomato plants is to mulch them heavily and feed them the right food (and much more often than I have in the past). I'd always wondered how to accomplish this since everything I'd ever read said to reduce water during fruiting, but with help given in this forum I discovered the wonders of foliar feeding with seaweed products. So, plant deeply if you plan to keep your plants off the ground (recommended), but don't forget the importance of feeding them what they need to thrive.
My plants are continuing to amaze me with their bounty, and I'm very grateful to all who've shared their experiences here! Where once I was lucky to get a handful of large tomatoes from each plant, to now where it's common to quickly get more than 20 from each one...sometimes even thirty(!), and they're still going strong.